Physics · NEET, JEE Main

Laws of Motion

210 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

180MCQ30Numerical76With diagram
Start with question 1 See it move: Laws of motion, friction and pulleysSee it move: Circular motion: banking and vertical circles
  1. 1A body of mass 2 kg2\,\text{kg} is acted upon by two perpendicular forces 6 N6\,\text{N} and 8 N8\,\text{N}. The magnitude of its acceleration is:NEET/MCQ/Medium
  2. 2A block m1=4 kgm_1 = 4\,\text{kg} on rough horizontal floor (μk=0.2\mu_k = 0.2) is connected to hanging mass m2=6 kgm_2 = 6\,\text{kg}. System acceleration is (g=10 m/s2g=10\,\text{m/s}^2):JEE Main/MCQ/Medium/With diagram
  3. 3Two blocks (PP and QQ) with respectively masses 22 kg and 1.51.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (SS), as shown in the figure below. Block PP is positioned on the top surface which has no friction and block QQ is in contact with side-surface, having coefficient friction μ\mu. The cube (SS) moves towards the right with acceleration of g2\dfrac{g}{2}, where gg is gravitational acceleration. During this movement the block PP and QQ remain stationary. The value of μ\mu is _______. (take g=10g = 10 m/s2^2)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  4. 4A wedge YY with mass of 1010 kg and all frictionless surfaces and the inclined surface making 37°37° with horizontal. A block XX with mass 22 kg is placed at the highest point of the wedge as shown in figure is at rest. At t=0t = 0 wedge (Y)(Y) is pulled toward right with constant force (f)(f) of 2424 N. Taking the block XX at rest at t=0t = 0, the time taken by it to slide down 8.88.8 m on the slope, while YY is on the move, is _____ s.
    (take     tan⁡(37°)=3/4\tan(37°) = 3/4 and g=10g = 10 m/s2^2)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  5. 5Three masses m1=4m_1 = 4 kg, m2=4m_2 = 4 kg and m3=6m_3 = 6 kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of T1/T2T_1/T_2 is _____.
    (take     g=10g = 10 m/s2^2)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  6. 6At t=0t=0, a body of mass 100100 g starts moving under the influence of a force (5i^+10j^)(5\hat{i}+10\hat{j}) N. After 22 s its position is (2xi^+5yj^)(2x\hat{i}+5y\hat{j}) m. The ratio x:yx:y is ______.JEE Main/MCQ/Medium/Newton's laws of motion
  7. 7A small block of mass mm slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration a0a_{0}. The angle between the inclined plane and ground is θ\theta and its base length is LL. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ____\_\_\_\_.
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  8. 8A particle of mass mm falls from rest through a resistive medium having resistive force, F=−kvF=-k v, where vv is the velocity of the particle and kk is a constant. Which of the following graphs represents velocity (vv) versus time (tt)?JEE Main/MCQ/Medium/Newton's laws of motion
  9. 9A 4 kg mass moves under the influence of a force F⃗=(4t3i^−3tj^)N\vec{F}=\left(4 t^{3} \hat{i}-3 t \hat{j}\right) \mathrm{N} where tt is the time in second. If mass starts from origin at t=0t=0, the velocity and position after t=2 st=2 \mathrm{~s} will be:JEE Main/MCQ/Medium/Newton's laws of motion
  10. 10An object with mass 500 g moves along x -axis with speed v=4x m/sv=4 \sqrt{x} \mathrm{~m} / \mathrm{s}. The force acting on the object is :JEE Main/MCQ/Medium/Newton's laws of motion
  11. 11A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time tt. Which of the following curve best describes acceleration of the block with time:JEE Main/MCQ/Medium/Newton's laws of motion
  12. 12A body of mass 4kg4kg experiences two forces F⃗1=5i^+8j^+7k^{\vec{F}}_{1}=5\hat{i}+8\hat{j}+7\hat{k} and F⃗2=3i^−4j^−3k.^{\vec{F}}_{2}=3\hat{i}-4\hat{j}-3\hat{k.} The acceleration acting on the body is:JEE Main/MCQ/Medium/Newton's laws of motion
  13. 13A cricket player catches a ball of mass 120g120g moving with 25ms−125m{s}^{-1} speed. If the catching process is completed in 0.1s0.1s then the magnitude of force exerted by the ball on the hand of player will be(in SI unit):JEE Main/MCQ/Medium/Newton's laws of motion
  14. 14Three blocks A,BA,B and CC are pulled on a horizontal smooth surface by a force of 80N80N as shown in figure. The tensions T1andT2{T}_{1}\text{and}{T}_{2} in the string are respectively:JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  15. 15The position vector of a particle related to time tt is given by r⃗=(10ti^+15t2j^+7k^)m\vec{r}=\left(10t\hat{i}+15{t}^{2}\hat{j}+7\hat{k}\right)m. The direction of net force experienced by the particle is :JEE Main/MCQ/Medium/Newton's laws of motion
  16. 16A body of mass 500g500g moves along xx-axis such that it's velocity varies with displacement xx according to the relation v=10xms−1v=10\sqrt{x}m{s}^{-1} the force acting on the body is:JEE Main/MCQ/Medium/Newton's laws of motion
  17. 17Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
    Assertion A : An electric fan continues to rotate for some time after the current is switched off.
    Reason R: Fan continues to rotate due to inertia of motion.
    In the light of above statements, choose the most appropriate answer from the options given below.    JEE Main/MCQ/Medium/Newton's laws of motion
  18. 18At any instant the velocity of a particle of mass 500g500g is (2ti^+3t2j^)ms−1\left(2t\hat{i}+3{t}^{2}\hat{j}\right)m{s}^{-1} . If the force acting on the particle at t=1st=1s is (i^+xj^)N(\hat{i}+x\hat{j})N . Then the value of xx will be:JEE Main/MCQ/Medium/Newton's laws of motion
  19. 19The figure represents the momentum time (p−t)(p-t) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ?
    If     (t3−t2)<t1\left({t}_{3}-{t}_{2}\right)\lt {t}_{1}
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  20. 20Force acts for 20s20s on a body of mass 20kg20kg, starting from rest, after which the force ceases and then body describes 50m50m in the next 10s10s. The value of force will be :JEE Main/MCQ/Medium/Newton's laws of motion
  21. 21Given below are two statements:
    Statement-I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
    Statement-II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.
    In the light of the above statements, choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Newton's laws of motion
  22. 22A uniform metal chain of mass mm and length LL passes over a massless and frictionless pulley. It is released from rest with a part of its length ll is hanging on one side and rest of its length L−lL-l is hanging on the other side of the pulley. At a certain point of time, when l=Lxl=\dfrac{L}{x}, the acceleration of the chain is g2\dfrac{g}{2}. The value of xx is _____.
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  23. 23A balloon has mass of 10g10g in air. The air escapes from the balloon at a uniform rate with velocity 4.5cms−14.5cm{s}^{-1}. If the balloon shrinks in 5s5s completely. Then, the average force acting on that balloon will be (in dyne).JEE Main/MCQ/Medium/Newton's laws of motion
  24. 24A block AA takes 2s2s to slide down a frictionless incline of 30∘30^{\circ} and length ll, kept inside a lift going up with uniform velocity vv. If the incline is changed to 45∘45^{\circ}, the time taken by the block, to slide down the incline, will be approximately:JEE Main/MCQ/Medium/Newton's laws of motion
  25. 25A block of mass MM slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ\theta. The magnitude of the contact force will be :JEE Main/MCQ/Medium/Newton's laws of motion
  26. 26Two masses M1{M}_{1} and M2{M}_{2} are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M2{M}_{2} is twice that of M1{M}_{1}. the acceleration of the system is a1{a}_{1}. When the mass M2{M}_{2} is thrice that of M1{M}_{1}. The acceleration of The system is a2{a}_{2}. The ratio a1a2\dfrac{{a}_{1}}{{a}_{2}} will be
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  27. 27A monkey of mass 50kg50kg climbs on a rope which can withstand the tension (T)\left(T\right) of 350N350N. If monkey initially climbs down with an acceleration of 4ms−24m{s}^{-2} and then climbs up with an acceleration of 5ms−25m{s}^{-2}. Choose the correct option (g=10ms−2)\left(g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/Newton's laws of motion
  28. 28Three masses M=100kg,m1=10kgM=100kg,{m}_{1}=10kg and m2=20kg{m}_{2}=20kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force FF is applied on the system so that the mass m2{m}_{2} moves upward with an acceleration of 2ms−22{ms}^{-2}. The value of FF is
    (Take     g=10ms−2g=10{ms}^{-2})
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  29. 29A block of metal weighing 2kg2kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1kgs−11kg{s}^{-1} and at a speed of 10ms−110{ms}^{-1}. Then, the initial acceleration of the block, in ms−2m{s}^{-2}, will be
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  30. 30A hanging mass MM is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2Mg2Mg force. In this situation, tension in the string is x5Mg\dfrac{x}{5}Mg for x=x=_____. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
    (Given     g=g= acceleration due to gravity)
    JEE Main/Numerical/Medium/Newton's laws of motion/With diagram
  31. 31A system to 1010 balls each of mass 2kg2kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th{7}^{th} and 8th{8}^{th} ball is _____ NN when 6th{6}^{th} ball just leaves the table.
    JEE Main/Numerical/Medium/Newton's laws of motion/With diagram
  32. 32A force on an object of mass 100g100g is (10i^+5j^)N\left(10\hat{i}+5\hat{j}\right)N. The position of that object at t=2st=2s is (ai^+bj^)m\left(a\hat{i}+b\hat{j}\right)m after starting from rest. The value of ab\dfrac{a}{b} will be _____ .JEE Main/Numerical/Medium/Newton's laws of motion
  33. 33The initial mass of a rocket is 1000kg1000kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of, 20ms−220{ms}^{-2}. The gases come out at a relative speed of 500ms−1500{ms}^{-1}, with respect to the rocket:
    [Useg=10ms−2]\left[\text{Use}g=10m{s}^{-2}\right]    JEE Main/MCQ/Medium/Newton's laws of motion
  34. 34A force F⃗=(40i^+10j^)N\vec{F}=(40\hat{i}+10\hat{j})N acts on a body of mass 5kg5kg. If the body starts from rest, its position vector r⃗\vec{r} at time t=10st=10s will beJEE Main/MCQ/Medium/Newton's laws of motion
  35. 35Two billiard balls of equal mass 30g30g strike a rigid wall with same speed of 108kmph108kmph (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball aa and ball bb by the wall along XX direction is:
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  36. 36A bullet of 4g4g mass is fired from a gun of mass 4kg.4kg. If the bullet moves with the muzzle speed of 50ms1,50{ms}^{1}, the impulse imparted to the gun and velocity of recoil of gun areJEE Main/MCQ/Medium/Newton's laws of motion
  37. 37A bullet of mass 0.1kg0.1kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50cm50cm into it. If the velocity of the bullet before hitting the wood is 10ms−110m{s}^{-1} and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is xN.xN. The value of xx to the nearest integer is,JEE Main/Numerical/Medium/Newton's laws of motion
  38. 38Consider a frame that is made up of two thin massless rods ABAB and ACAC as shown in the figure. A vertical force P⃗\vec{P} of magnitude 100N100N is applied at point AA of the frame.

    Suppose the force is     P⃗\vec{P} resolved parallel to the arms ABAB and ACAC of the frame. The magnitude of the resolved component along the arm ACAC is xNxN. The value of xx, to the nearest integer, is ________.
    [Given :     sin⁡(35∘)=0.573,cos⁡(35∘)=0.819,sin⁡(110∘)=0.939,cos⁡(110∘)=−0.342\sin \left(35^{\circ}\right)=0.573,\cos \left(35^{\circ}\right)=0.819,\sin \left(110^{\circ}\right)=0.939,\cos \left(110^{\circ}\right)=-0.342]    JEE Main/Numerical/Medium/Newton's laws of motion/With diagram
  39. 39Two masses AA and BB, each of mass MM are fixed together by a massless spring, A force acts on the mass BB as shown in figure. If the mass AA starts moving away from mass BB with acceleration aa, then the acceleration of mass BB will be :
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  40. 40A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dM(t)dt=bv2(t),\dfrac{dM(t)}{dt}=b{v}^{2}(t), where v(t)v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:JEE Main/MCQ/Medium/Newton's laws of motion
  41. 41A mass of 10kg10kg is suspended by a rope of length 4m4m, from the ceiling. A force FF is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45∘45^{\circ} with the vertical. Then FF equals: (Take g=10ms−2g=10m{s}^{-2} and the rope to be massless)JEE Main/MCQ/Medium/Newton's laws of motion
  42. 42A block of mass 5kg5kg is (i) pushed in case (A)\left(A\right) and (ii) pulled in case (B),\left(B\right), by a force F=20N,F=20N, making an angle of 30o{30}^{o} with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is μ=0.2.\mu =0.2. The difference between the accelerations of the block, in case (B)\left(B\right) and case (A)\left(A\right) will be:
    (g=10ms−2)\left(g=10 m{s}^{-2}\right)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  43. 43A ball is thrown upward with an initial velocity V0{V}_{0} from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2m\gamma {v}^{2} (where mm is mass of the ball, vv is its instantaneous velocity and γ\gamma is a constant). Time taken by the ball to rise to its zenith is:JEE Main/MCQ/Medium/Newton's laws of motion
  44. 44A vertical closed cylinder is separated into two parts by a frictionless piston of mass mm and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is l1,{l}_{1}, and that below the piston is l2,{l}_{2}, such that l1>l2.{l}_{1}\gt {l}_{2}. Each part of the cylinder contains nn moles of an ideal gas at equal temperature T.T. If the piston is stationary, its mass mm will be given by:

    (    RR is universal gas constant and gg is the acceleration due to gravity)    JEE Main/MCQ/Medium/Newton's laws of motion
  45. 45A particle of mass m\mathrm{m} is moving in a straight line with momentum p. Starting at time t=0,t=0, a force F=kF=k t acts in the same direction on the moving particle during time interval T so that its momentum changes from p\mathrm{p} to 3p3 \mathrm{p}. Here kk is a constant. The value of T\mathrm{T} isJEE Main/MCQ/Medium/Newton's laws of motion
  46. 46The machine as shown has 22 rods of length 1m1m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a 2kg2kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  47. 47A conical pendulum of length ll makes an angle θ=45∘\theta =45^{\circ} with respect to Z−Z-axis and moves in a circle in the XYXY plane. The radius of the circle is 0.4m0.4m and its center is vertically below OO. The speed of the pendulum, in its circular path, will be - (Takeg=10ms−2)\left(Takeg=10m{s}^{-2}\right)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  48. 48A particle of mass mm is acted upon by a force FF given by the empirical law F=Rt2v(t).F=\dfrac{R}{{t}^{2}}v\left(t\right). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plotJEE Main/MCQ/Medium/Newton's laws of motion
  49. 49Which of the following option correctly describes the variation of the speed υυ and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F=−kυF=-kυ , where 'k' is a constant, on the body? (Graphs are schematic and not drown to scale)JEE Main/MCQ/Medium/Newton's laws of motion
  50. 50A large number (n)(n) of identical beads, each of mass mm and radius rr are strung on a thin smooth rigid horizontal rod of length L(L≫r)L(L≫r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed vv, the average force experienced by each support after a long time is (assume all collisions are elastic):
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  51. 51A body of mass 5 kg5 \mathrm{~kg} under the action of constant force F⃗=Fxi^+Fyj^\vec{F}=F_x \hat{i}+F_y \hat{j} has velocity at t=0 s\mathrm{t}=0 \mathrm{~s} as v→=(6i^−2j^m/s)\overrightarrow{\mathrm{v}}=(6 \hat{\mathrm{i}}-2 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}) and at t=10 s\mathrm{t}=10 \mathrm{~s} as v→=+6j^m/s\overrightarrow{\mathrm{v}}=+6 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}. The force F→\overrightarrow{\mathrm{F}} is:JEE Main/MCQ/Medium/Newton's laws of motion
  52. 52Water is flowing at a speed of 1.5 m s-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = 103 kg m-3)JEE Main/MCQ/Medium/Newton's laws of motion
  53. 53Two blocks of mass M1=20 kgM_1=20 \mathrm{~kg} and M2=12 kgM_2=12 \mathrm{~kg} are connected by a metal rod of mass 8 kg8 \mathrm{~kg}. The system is pulled vertically up by applying a force of 480 N480 \mathrm{~N} as shown. The tension at the mid-point of the rod is:
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  54. 54This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements.
    Statement 1: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force.
    Statement 2: The cart does not move because the force described in statement 1 cancel each other.    JEE Main/MCQ/Medium/Newton's laws of motion
  55. 55A satellite moving with velocity vv in a force free space collects stationary interplanetary dust at a rate of dMdt=αv\frac{d M}{d t}=\alpha v where MM is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite isJEE Main/MCQ/Medium/Newton's laws of motion
  56. 56Sand is being dropped on a conveyer belt at the rate of 2 kg2 \mathrm{~kg} per second. The force necessary to keep the belt moving with a constant speed of 3 ms−13 \mathrm{~ms}^{-1} will beJEE Main/MCQ/Medium/Newton's laws of motion
  57. 57An engine pumps water continuously through a hose. Water leaves the hose with velocity vv and mm is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface isJEE Main/MCQ/Medium/Newton's laws of motion
  58. 58A car of mass 1000 kg1000 \mathrm{~kg} is moving at a speed of 30 m/s\mathrm{m} / \mathrm{s}. Brakes are applied to bring the car to rest. If the net retarding force is 5000 N5000 \mathrm{~N}, the car comes to stop after travelling d md \mathrm{~m} in t st \mathrm{~s}. ThenJEE Main/MCQ/Medium/Newton's laws of motion
  59. 59A particle of mass m\mathrm{m} is at rest at the origin at time t=0\mathrm{t}=0. It is subjected to a force F(t)=F0e−bt\mathrm{F}(\mathrm{t})=\mathrm{F}_0 \mathrm{e}^{-\mathrm{bt}} in the xx direction. Its speed v(t)v(t) is depicted by which of the following curves?JEE Main/MCQ/Medium/Newton's laws of motion
  60. 60Two fixed frictionless inclined plane making an angle 30∘30^{\circ} and 60∘60^{\circ} with the vertical are shown in the figure. Two block AA and BB are placed on the two planes. What is the relative vertical acceleration of AA with respect to BB ?
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  61. 61A body weighing 13 kg13 \mathrm{~kg} is suspended by two strings 5 m5 \mathrm{~m} and 12 m12 \mathrm{~m} long, their other ends being fastened to the extremities of a rod 13 m13 \mathrm{~m} long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings areJEE Main/MCQ/Medium/Newton's laws of motion
  62. 62A player caught a cricket ball of mass 150 g150 \mathrm{~g} moving at a rate of 20 m/s20 \mathrm{~m} / \mathrm{s}. If the catching process is completed in 0.1 s0.1 \mathrm{~s}, the force of the blow exerted by the ball on the hand of the player is equal toJEE Main/MCQ/Medium/Newton's laws of motion
  63. 63A particle of mass 0.3 kg0.3 \mathrm{~kg} is subjected to a force F=−kxF=-k x with k=15 N/mk=15 \mathrm{~N} / \mathrm{m}. What will be its initial acceleration if it is released from a point 20 cm20 \mathrm{~cm} away from the origin?JEE Main/MCQ/Medium/Newton's laws of motion
  64. 64Two masses m1=5 kgm_1=5 \mathrm{~kg} and m2=4.8 kgm_2=4.8 \mathrm{~kg} tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move (g=9.8 m/s2)\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  65. 65A machine gun fires a bullet of mass 40 g40 \mathrm{~g} with a velocity 1200 ms−11200 \mathrm{~ms}^{-1}. The man holding it can exert a maximum force of 144 N144 \mathrm{~N} on the gun. How many bullets can he fire per second at the most?JEE Main/MCQ/Medium/Newton's laws of motion
  66. 66A rocket with a lift-off mass 3.5×104 kg3.5 \times 10^4 \mathrm{~kg} is blasted upwards with an initial acceleration of 10 m/s210 \mathrm{~m} / \mathrm{s}^2. Then the initial thrust of the blast isJEE Main/MCQ/Medium/Newton's laws of motion
  67. 67A block of mass MM is pulled along a horizontal frictionless surface by a rope of mass m\mathrm{m}. If a force P\mathrm{P} is applied at the free end of the rope, the force exerted by the rope on the block isJEE Main/MCQ/Medium/Newton's laws of motion
  68. 68Three forces start acting simultaneously on a particle moving with velocity, v→\overrightarrow{\mathrm{v}}. These forces are represented in magnitude and direction by the three sides of a triangle ABC\mathrm{ABC}. The particle will now move with velocity
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  69. 69A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N\mathrm{N}, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s25 \mathrm{~m} / \mathrm{s}^2, the reading of the spring balance will beJEE Main/MCQ/Medium/Newton's laws of motion
  70. 70Three identical blocks of masses m=2 kg\mathrm{m}=2 \mathrm{~kg} are drawn by a force F=10.2 N\mathrm{F}=10.2 \mathrm{~N} with an acceleration of 0.6 ms−20.6 \mathrm{~ms}^{-2} on a frictions surface, then what is the tension (in N\mathrm{N} ) in the string between the blocks BB and CC?
    JEE Main/MCQ/Medium/Newton's laws of motion/With diagram
  71. 71When forces F1,F2,F3F_1, F_2, F_3 are acting on a particle of mass mm such that F2F_2 and F3F_3 are mutually perpendicular, then the particle remains stationary. If the force F1F_1 is now removed then the acceleration of the particle isJEE Main/MCQ/Medium/Newton's laws of motion
  72. 72A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the
    ball as observed by the man in the lift and a man standing stationary on the ground are respectively    JEE Main/MCQ/Medium/Newton's laws of motion
  73. 73A flexible chain of mass mm hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is 30∘30^{\circ}. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is ____\_\_\_\_.JEE Main/MCQ/Medium/Equilibrium of Forces
  74. 74A body of mass mm is suspended by two strings making angles θ1\theta_1 and θ2\theta_2 with the horizontal ceiling with tensions T1T_1 and T2T_2 simultaneously. T1T_1 and T2T_2 are related by T1=3T2T_1=\sqrt{3} T_2. the angles θ1\theta_1 and θ2\theta_2 areJEE Main/MCQ/Medium/Equilibrium of Forces
  75. 75
    A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions     T1T_1 and T2T_2, respectively, are (in N) :    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  76. 76

    A string of length     LL is fixed at one end and carries a mass of MM at the other end. The mass makes (3π)\left(\frac{3}{\pi}\right) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ……\ldots\ldots ML.    JEE Main/Numerical/Medium/Equilibrium of Forces/With diagram
  77. 77A 1 kg1 \mathrm{~kg} mass is suspended from the ceiling by a rope of length 4 m4 \mathrm{~m}. A horizontal force ' FF ' is applied at the mid point of the rope so that the rope makes an angle of 45∘45^{\circ} with respect to the vertical axis as shown in figure. The magnitude of FF is :
    (Assume that the system is in equilibrium and     g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2 )
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  78. 78A light unstretchable string passing over a smooth light pulley connects two blocks of masses m1m_1 and m2m_2. If the acceleration of the system is g8\frac{g}{8}, then the ratio of the masses m2m1\frac{m_2}{m_1} is :JEE Main/MCQ/Medium/Equilibrium of Forces
  79. 79A body of weight 200 N200 \mathrm{~N} is suspended from a tree branch through a chain of mass 10 kg10 \mathrm{~kg}. The branch pulls the chain by a force equal to (if g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2 ) :JEE Main/MCQ/Medium/Equilibrium of Forces
  80. 80A light string passing over a smooth light pulley connects two blocks of masses m1m_1 and m2m_2 (where m2>m1m_2\gt m_1 ). If the acceleration of the system is g2\frac{g}{\sqrt{2}}, then the ratio of the masses m1m2\frac{m_1}{m_2} is:JEE Main/MCQ/Medium/Equilibrium of Forces
  81. 81Three blocks M1,M2,M3M_1, M_2, M_3 having masses 4 kg,6 kg4 \mathrm{~kg}, 6 \mathrm{~kg} and 10 kg10 \mathrm{~kg} respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope 1,T11, T_1 when they are moving upward with acceleration of 2 ms−22 \mathrm{~ms}^{-2} is _____N(\mathrm{N}\left(\right. if g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ).
    JEE Main/Numerical/Medium/Equilibrium of Forces/With diagram
  82. 82A wooden block of mass 5 kg5 \mathrm{~kg} rests on a soft horizontal floor. When an iron cylinder of mass 25 kg25 \mathrm{~kg} is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 ms−20.1 \mathrm{~ms}^{-2}. The action force of the system on the floor is equal to:JEE Main/MCQ/Medium/Equilibrium of Forces
  83. 83A light string passing over a smooth light fixed pulley connects two blocks of masses m1{m}_{1} and m2{m}_{2}. If the acceleration of the system is g8\dfrac{g}{8}, then the ratio of masses isJEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  84. 84All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2kg2kg is:JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  85. 85A stone of mass 900g900g is tied to a string and moved in a vertical circle of radius 1m1m making 10rpm10rpm. The tension in the string, when the stone is at the lowest point is (if π2=9.8{\pi }^{2}=9.8 and g=9.8ms−2g=9.8m{s}^{-2})JEE Main/MCQ/Medium/Equilibrium of Forces
  86. 86As shown in the figure a block of mass 10kg10kg lying on a horizontal surface is pulled by a force F acting at an angle 30∘30^{\circ}, with horizontal. For μs=0.25{\mu }_{s}=0.25, the block will just start to move for the value of FF: [Given g =10m⋅s–2=10m\cdot {s}^{–2}]JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  87. 87As shown in figure, a 70kg70kg garden roller is pushed with a force of F⃗=200N\vec{F}=200N at an angle of 30∘30^{\circ} with horizontal. The normal reaction on the roller is (Given g=10ms−2g=10m{s}^{-2})
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  88. 88A block of 3kg\sqrt{3}kg is attached to a string whose other end is attached to the wall. An unknown force FF is applied so that the string makes an angle of 30∘30^{\circ} with the wall. The tension TT is : (Given g =10ms–2=10m{s}^{–2})
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  89. 89As per given figure, a weightless pulley PP is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if g=10ms−2g=10m{s}^{-2})
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  90. 90Two bodies of masses m1=5kg{m}_{1}=5kg and m2=3kg{m}_{2}=3kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m1{m}_{1} will be : [Take g=10ms−2g=10m{s}^{-2}]
    ​​​​​​​    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  91. 91For a free body diagram shown in the figure, the four forces are applied in the 'xx' and 'yy' directions. What additional force must be applied and at what angle with positive xx-axis so that the net acceleration of body is zero?
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  92. 92Four forces are acting at a point PP in equilibrium as shown in figure. The ratio of force F1{F}_{1} to F2{F}_{2} is 1:x1:x where x=x=_____ .
    JEE Main/Numerical/Medium/Equilibrium of Forces/With diagram
  93. 93A block of mass MM placed inside a box descends vertically with acceleration aa. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ′a′'a' will beJEE Main/MCQ/Medium/Equilibrium of Forces
  94. 94A mass of 10kg10kg is suspended vertically by a rope of length 5m5m from the roof. A force of 30N30N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is α=tan⁡−1(x×10−1)\alpha ={\tan }^{-1}\left(x\times {10}^{-1}\right). The value of xx is _____ .
    (Given,     g=10ms−2g=10m{s}^{-2})    JEE Main/Numerical/Medium/Equilibrium of Forces
  95. 95In the arrangement shown in figure a1,a2,a3{a}_{1},{a}_{2},{a}_{3} and a4{a}_{4} are the accelerations of masses m1,m2,m3{m}_{1},{m}_{2},{m}_{3} and m4{m}_{4} respectively. Which of the following relation is true for this arrangement?
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  96. 96A block of mass 200g200g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F=xNF=\sqrt{x}N as shown in figure.

    The value of     x=_____.    JEE Main/Numerical/Medium/Equilibrium of Forces/With diagram
  97. 97A block of mass mm slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is:
    Given     m=8kg,M=16kgm=8kg,M=16kg
    Assume all the surfaces shown in the figure to be frictionless.
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  98. 98A car is moving on a plane inclined at 30∘30^{\circ} to the horizontal with an acceleration of 10ms−210{ms}^{-2} parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take g=10ms−2g=10{ms}^{-2})JEE Main/Numerical/Medium/Equilibrium of Forces
  99. 99The boxes of masses 2kg2kg and 8kg8kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8kg8kg to strike the ground starting from rest. (g=10ms−2)\left(g=10m{s}^{-2}\right)
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  100. 100A particle is moving with uniform speed along the circumference of a circle of radius RR under the action of a central fictitious force FF which is inversely proportional to R3{R}^{3}. Its time period of revolution will be given by :JEE Main/MCQ/Medium/Equilibrium of Forces
  101. 101A block of mass mm is kept on a platform which starts from rest with a constant acceleration g/2g/2 upwards, as shown in the figure. Work done by normal reaction on block in time tt is

    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  102. 102A mass of 10kg10kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45∘45^{\circ} at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g=10ms−2)\left(g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/Equilibrium of Forces
  103. 103A block of mass 10kg10kg is kept on a rough inclined plane as shown in the figure. A force of 3N3N is applied on the block. The coefficient of static friction between the plane and the block is 0.6.0.6. What should be the minimum value of force P,P, such that the block does not move downward? (take g=10ms−2g=10m{s}^{-2} )

    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  104. 104As shown in the figure, forces of 105 N10^5 \mathrm{~N} each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm10 \mathrm{~cm}, shifting the upper face parallel to itself by 0.5 cm0.5 \mathrm{~cm}. If the side of another cube of the same material is, 20 cm20 \mathrm{~cm} then under similar conditions as above, the displacement will be:
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  105. 105A uniform cylinder of length L\text{L} and mass M\text{M} having cross-sectional area A\text{A} is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ\sigma at equilibrium position. The extension x0{\text{x}}_{0} of the spring when it is in equilibrium is :JEE Main/MCQ/Medium/Equilibrium of Forces
  106. 106A mass of Mkg\mathrm{M} \mathrm{kg} is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45∘45^{\circ} with the initial vertical direction isJEE Main/MCQ/Medium/Equilibrium of Forces
  107. 107A block is kept on a frictionless inclined surface with angle of inclination α\alpha. The incline is given an acceleration a to keep the block stationary. Then a is equal to
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  108. 108One end of a massless rope, which passes over a massless and frictionless pulley PP is tied to a hook CC while the other end is free. Maximum tension that the rope can bear is 360 N360 \mathrm{~N}. With what value of maximum safe acceleration (in ms−2\mathrm{ms}^{-2} ) can a man of 60 kg60 \mathrm{~kg} climb on the rope?
    JEE Main/MCQ/Medium/Equilibrium of Forces/With diagram
  109. 109A light string passing over a smooth light pulley connects two blocks of masses m1m_1 and m2m_2 (vertically). If the acceleration of the system is g/8\mathrm{g} / 8, then the ratio of the masses isJEE Main/MCQ/Medium/Equilibrium of Forces
  110. 110A spring of force constant 15 N/m15 \mathrm{~N} / \mathrm{m} is cut into two pieces. If the ratio of their length is 1:31: 3, then the force constant of smaller piece is ____\_\_\_\_ N/m\mathrm{N} / \mathrm{m}.JEE Main/MCQ/Medium/Spring force
  111. 111The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.JEE Main/Numerical/Medium/Spring force
  112. 112A massless spring gets elongated by amount x1x_1 under a tension of 5 N . Its elongation is x2x_2 under the tension of 7 N . For the elongation of (5x1−2x2)\left(5 x_1-2 x_2\right), the tension in the spring will be,JEE Main/MCQ/Medium/Spring force
  113. 113A small block of mass 100g100g is tied to a spring of spring constant 7.5Nm−17.5N{m}^{-1} and length 20cm.20cm. The other end of spring is fixed at a particular point A.A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5rads−15rad{s}^{-1}about point A,A, then tension in the spring isJEE Main/MCQ/Medium/Spring force
  114. 114A mass mm is attached to two springs as shown in figure. The spring constants of two springs are K1{K}_{1} and K2.{K}_{2}. For the frictionless surface, the time period of oscillation of mass mm is
    JEE Main/MCQ/Medium/Spring force/With diagram
  115. 115A body of mass 200g200g is tied to a spring of spring constant 12.5Nm−112.5N{m}^{-1}, while the other end of spring is fixed at point OO. If the body moves about OO in a circular path on a smooth horizontal surface with constant angular speed 5rads−15rad{s}^{-1}, then the ratio of extension in the spring to its natural length will be :JEE Main/MCQ/Medium/Spring force
  116. 116One end of a massless spring of spring constant kk and natural length l0{l}_{0} is fixed while the other end is connected to a small object of mass mm lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity ω\omega about an axis passing trough fixed end, then the elongation of the spring will beJEE Main/MCQ/Medium/Spring force
  117. 117The motion of a mass on a spring, with spring constant KK is as shown in figure.

    The equation of motion is given by,     x(t)=Asin⁡ωt+x(t)=A\sin \omega t+Bcos⁡ωtB\cos \omega t with ω=Km\omega =\sqrt{\dfrac{K}{m}}.
    Suppose that at time     t=0,t=0,the position of mass is x(0)x(0) and velocity v(0),v(0), then its displacement can also be represented as x(t)=Ccos⁡(ωt−ϕ),x(t)=C\cos (\omega t-\phi ), where CC and ϕ\phi are    JEE Main/MCQ/Medium/Spring force/With diagram
  118. 118Two identical blocks AA and BB each of mass mm resting on the smooth horizontal floor are connected by a light spring of natural length LL and spring constant KK. A third block CC of mass mm moving with a speed vv along the line joining AA and BB collides with AA.The maximum compression in the spring is
    JEE Main/MCQ/Medium/Spring force/With diagram
  119. 119If two similar springs each of spring constant K1{K}_{1} are joined in series, the new spring constant and time period would be changed by a factor:JEE Main/MCQ/Medium/Spring force
  120. 120A particle of mass mm is fixed to one end of a light spring having force constant kk and unstretched length l.l. The other end is fixed. The system is given an angular speed ω\omega about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:JEE Main/MCQ/Medium/Spring force
  121. 121A spring whose unstrentches length is ll has a force constant k.k. The spring is cut into two pieces of unstretches lengths l1{l}_{1} and l2{l}_{2} where, l1=nl2{l}_{1}=n{l}_{2} and nn is an integer. The ratio k1/k2{k}_{1}/{k}_{2} of the corresponding force constants, k1{k}_{1} and k2{k}_{2} will be:JEE Main/MCQ/Medium/Spring force
  122. 122This question has statement 11 and statement 22. Of the four choices given after the statements, choose the one that best describes the two statements.
    If two springs     S1\mathrm{S_1} and S2\mathrm{S_2} of force constants k1k_1 and k2k_2, respectively, are stretched by the same force, it is found that more work is done on spring S1\mathrm{S_1} than on spring S2\mathrm{S_2}.
    Statement     11 : If stretched by the same amount, work done on S1\mathrm{S}_1, will be more than that on S2\mathrm{S}_2
    Statement     2:k1<k22: k_1 \lt k_2    JEE Main/MCQ/Medium/Spring force
  123. 123A 2 kg2 \mathrm{~kg} block slides on a horizontal floor with a speed of 4 m/s4 \mathrm{~m} / \mathrm{s}. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N15 \mathrm{~N} and spring constant is 10,000.N/m10,000 . \mathrm{N} / \mathrm{m}. The spring compresses byJEE Main/MCQ/Medium/Spring force
  124. 124A block of mass ' m\mathrm{m} ' is connected to another block of mass ' M\mathrm{M} ' by a spring (massless) of spring constant ' k\mathrm{k} '. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force 'F\mathrm{F}' starts acting on the block of mass 'M\mathrm{M}' to pull it. Find the force on the block of mass 'm\mathrm{m}'JEE Main/MCQ/Medium/Spring force
  125. 125A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading isJEE Main/MCQ/Medium/Spring force
  126. 126A block takes tt time to slide down a plane inclined at 45°45° to the horizontal. If the surface is made smooth (frictionless), the block takes time t2\dfrac{t}{2} to slide down the plane. The coefficient of friction between the block and the inclined plane is (α100)\left(\dfrac{\alpha}{100}\right). The value of α\alpha is __________.JEE Main/Numerical/Medium/Frictional force
  127. 127A mass of 1 kg1\text{ kg} is kept on an inclined plane with 30°30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s4\text{ m/s}. The work done by the frictional force in time 2 s2\text{ s} is _______ J. (Take g=10 m/s2g = 10\text{ m/s}^2)JEE Main/MCQ/Medium/Frictional force
  128. 128The time taken by a block of mass mm to slide down from the highest point to the lowest point on a rough inclined plane is 50%50\% more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45∘45^\circ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.JEE Main/MCQ/Medium/Frictional force
  129. 129A 0.50.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 44 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 55 rad/s. The coefficient of friction between the drum's inner wall surface and mass is _______. (Take g=10g = 10 m/s2^2)JEE Main/MCQ/Medium/Frictional force
  130. 130A block of mass 5 kg is moving on an inclined plane which makes an angle of 30∘30^{\circ} with the horizontal. Friction coefficient between the block and inclined plane surface is 32\frac{\sqrt{3}}{2}. The force to be applied on the block so that the block will move down without acceleration is ____\_\_\_\_ N.
    (g=10 m/s2)\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right).    JEE Main/MCQ/Medium/Frictional force
  131. 131In the given figure the blocks A,BA, B and CC weigh 4 kg,6 kg4 \mathrm{~kg}, 6 \mathrm{~kg} and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force F⃗\vec{F} required to slide the block CC with constant speed is ____\_\_\_\_ N.
    (Use     g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^{2})
    JEE Main/Numerical/Medium/Frictional force/With diagram
  132. 132A block is sliding down on an inclined plane of slope θ\theta and at an instant t=0t=0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity uu. The distance (S)(S) travelled by the block before its velocity become zero, is ____\_\_\_\_.
    (    g=g= gravitational acceleration)    JEE Main/MCQ/Medium/Frictional force
  133. 133A large drum having radius RR is spinning around its axis with angular velocity ω\omega, as shown in figure. The minimum value of ω\omega so that a body of mass MM remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass MM as μ\mu, is :
    JEE Main/MCQ/Medium/Frictional force/With diagram
  134. 134A cubic block of mass mm is sliding down on an inclined plane at 60∘60^{\circ} with an acceleration of g2\frac{\mathrm{g}}{2}, the value of coefficient of kinetic friction isJEE Main/MCQ/Medium/Frictional force
  135. 135A given object takes n\mathrm{n} times the time to slide down 45∘45^{\circ} rough inclined plane as it takes the time to slide down an identical perfectly smooth 45∘45^{\circ} inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :JEE Main/MCQ/Medium/Frictional force
  136. 136A heavy box of mass 50 kg50 \mathrm{~kg} is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :JEE Main/MCQ/Medium/Frictional force
  137. 137A 2 kg2 \mathrm{~kg} brick begins to slide over a surface which is inclined at an angle of 45∘45^{\circ} with respect to horizontal axis. The co-efficient of static friction between their surfaces is:JEE Main/MCQ/Medium/Frictional force
  138. 138Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.040.04, the acceleration of the system in ms−2m{s}^{-2} is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :JEE Main/MCQ/Medium/Frictional force/With diagram
  139. 139A block of mass 5kg5kg is placed on a rough inclined surface as shown in the figure. If F⃗1{\vec{F}}_{1} is the force required to just move the block up the inclined plane and F⃗2{\vec{F}}_{2} is the force required to just prevent the block from sliding down, then the value of ∣F⃗1∣−∣F⃗2∣\left|{\vec{F}}_{1}\right|-\left|{\vec{F}}_{2}\right| is: [Use g=10ms−2g=10m{s}^{-2}]JEE Main/MCQ/Medium/Frictional force/With diagram
  140. 140A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ\mu. If the distance of the coin from the center of the disc is rr, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :JEE Main/MCQ/Medium/Frictional force
  141. 141In the given arrangement of a doubly inclined plane two blocks of masses MM and mm are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.250.25. The value of mm, for which M=10kgM=10kg will move down with an acceleration of 2ms−22m{s}^{-2}, is: (take g=10ms−2g=10m{s}^{-2} and tan⁡37∘=34\tan 37^{\circ}=\dfrac{3}{4})JEE Main/MCQ/Medium/Frictional force/With diagram
  142. 142A block of mass mm is placed on a surface having vertical cross section given by y=x24y=\dfrac{{x}^{2}}{4}. If coefficient of friction is 0.50.5, the maximum height above the ground at which block can be placed without slipping is:JEE Main/MCQ/Medium/Frictional force
  143. 143Given below are two statements :
    Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.
    Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Frictional force
  144. 144A coin placed on a rotating table just slips when it is placed at a distance of 1cm1cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre:JEE Main/MCQ/Medium/Frictional force
  145. 145A block of mass 5kg5kg is placed at rest on a table of rough surface. Now, if a force of 30N30N is applied in the direction parallel to surface of the table, the block slides through a distance of 50m50m in an interval of time 10s10s. Coefficient of kinetic friction is (given, g=10ms–2g=10m{s}^{–2} ):JEE Main/MCQ/Medium/Frictional force
  146. 146A body of mass 10kg10kg is moving with an initial speed of 20ms−120m{s}^{-1}. The body stops after 5s5s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity g=10ms−2g=10m{s}^{-2})JEE Main/MCQ/Medium/Frictional force
  147. 147The time taken by an object to slide down 45∘45^{\circ} rough inclined plane is nn times as it takes to slide down a perfectly smooth 45∘45^{\circ} incline plane. The coefficient of kinetic friction between the object and the incline plane is:JEE Main/MCQ/Medium/Frictional force
  148. 148A block of mass mm slides down the plane inclined at angle 30∘30^{\circ} with an acceleration g4\dfrac{g}{4} . The value of coefficient of kinetic friction will be :JEE Main/MCQ/Medium/Frictional force
  149. 149Consider a block kept on an inclined plane (inclined at 45∘45^{\circ}) as shown in the figure. If the force required to just push it up the incline is 22 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (µ)(µ) is equal to :
    .    JEE Main/MCQ/Medium/Frictional force/With diagram
  150. 150A bag is gently dropped on a conveyor belt moving at a speed of 2ms−12m{s}^{-1}. The coefficient of friction between the conveyor belt and bag is 0.40.4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take g=10ms−2g=10m{s}^{-2}]JEE Main/MCQ/Medium/Frictional force
  151. 151A block of mass 40kg40kg slides over a surface, when a mass of 4kg4kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.
    The coefficient of kinetic friction between the surface and block is     0.020.02. The acceleration of block is: (Given g=10ms−2g=10{ms}^{-2}.)
    JEE Main/MCQ/Medium/Frictional force/With diagram
  152. 152A block of mass 2kg2kg moving on a horizontal surface with speed of 4ms−14{ms}^{-1} enters a rough surface ranging from x=0.5mx=0.5m to x=1.5mx=1.5m. The retarding force in this range of rough surface is related to distance by F=−kxF=-kx where k=12Nm−1k=12N{m}^{-1}. The speed of the block as it just crosses the rough surface will beJEE Main/MCQ/Medium/Frictional force
  153. 153A system of two blocks of masses m=2kgm=2kg and M=8kgM=8kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.50.5. The maximum horizontal force FF that can be applied to the block of mass MM so that the blocks move together will be (g=9.8ms−2)\left(g=9.8m{s}^{-2}\right)
    JEE Main/MCQ/Medium/Frictional force/With diagram
  154. 154A disc with a flat small bottom beaker placed on it at a distance RR from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity ω\omega. The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ\mu. The beaker will revolve with the disc if :JEE Main/MCQ/Medium/Frictional force
  155. 155A uniform chain of 6m6m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.50.5, the maximum length of the chain hanging from the table is _____ mm.JEE Main/Numerical/Medium/Frictional force
  156. 156A block of mass 10kg10kg starts sliding on a surface with an initial velocity of 9.8ms−19.8{ms}^{-1}. The coefficient of friction between the surface and block is 0.50.5. The distance covered by the block before coming to rest is :[use g=9.8ms−2g=9.8{ms}^{-2}]JEE Main/MCQ/Medium/Frictional force
  157. 157The average translational kinetic energy of N2{N}_{2} gas molecules at _________C^{\circ} becomes equal to the K.E.K.E. of an electron accelerated from rest through a potential difference of 0.1volt.0.1volt.
    (Given     kB=1.38×10−23JK−1)\left.{k}_{B}=1.38\times {10}^{-23}J{K}^{-1}\right) (Fill the nearest integer).    JEE Main/Numerical/Medium/Frictional force
  158. 158The coefficient of static friction between two blocks is 0.50.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _______NN (take g=10ms−2)\left.g=10{ms}^{-2}\right)
    JEE Main/Numerical/Medium/Frictional force/With diagram
  159. 159A body of mass mm is launched up on a rough inclined plane making an angle of 30∘30^{\circ} with the horizontal. The coefficient of friction between the body and plane is x5\dfrac{\sqrt{x}}{5} if the time of ascent is half of the time of descent. The value of xx isJEE Main/Numerical/Medium/Frictional force
  160. 160A steel block of 10kg10kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2ms−2.0.2m{s}^{-2}. The normal reaction R′{R}^{'} by the floor if mass of the iron cylinders are equal and of 20kg20kg each is (inN)\left(\text{in}N\right),
    [Take     g=10ms−2g=10m{s}^{-2} and μs=0.2]\left.{\mu }_{s}=0.2\right]
    JEE Main/MCQ/Medium/Frictional force/With diagram
  161. 161A boy of mass 4kg4kg is standing on a piece of wood having mass 5kg5kg. If the coefficient of friction between the wood and the floor is 0.5,0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _______ NN. (Round off to the Nearest Integer)
    [Take     g=10ms−2]\left.g=10{ms}^{-2}\right]
    JEE Main/Numerical/Medium/Frictional force/With diagram
  162. 162A body of mass 1kg1kg rests on a horizontal floor with which it has a coefficient of static friction 13\dfrac{1}{\sqrt{3}}. It is desired to make the body move by applying the minimum possible force FNFN. The value of FF will be _______.(Round off to the Nearest Integer) [Take g=10ms−2g=10{ms}^{-2} ]JEE Main/Numerical/Medium/Frictional force
  163. 163Two blocks (m=0.5kgm=0.5kg and M=4.5kgM=4.5kg) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is 37.\dfrac{3}{7}. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is N.N. (Round off to the Nearest Integer) [Take gg as 9.8ms−29.8m{s}^{-2}]
    JEE Main/Numerical/Medium/Frictional force/With diagram
  164. 164A block of mass mm slides along a floor while a force of magnitude FF is applied to it at an angle θ\theta as shown in figure. The coefficient of kinetic friction is μK{\mu }_{K}. Then, the block's acceleration aa is given by : (gg is acceleration due to gravity)
    JEE Main/MCQ/Medium/Frictional force/With diagram
  165. 165An inclined plane making an angle of 30∘30^{\circ} with the horizontal is placed in a uniform horizontal electric field 200NC200\dfrac{N}{C} as shown in the figure. A body of mass 1kg1kg and charge 5mC5mC is allowed to slide down from rest at a height of 1m1m. If the coefficient of friction is 0.2,0.2, find the time taken by the body to reach the bottom.
    [g=9.8ms−2;sin⁡30∘=12;cos⁡30∘=32]\left[g=9.8m{s}^{-2};\sin 30^{\circ}=\dfrac{1}{2};\cos 30^{\circ}=\dfrac{\sqrt{3}}{2}\right]
    JEE Main/MCQ/Medium/Frictional force/With diagram
  166. 166As shown in the figure, a block of mass 3kg\sqrt{3}kg is kept on a horizontal rough surface of coefficient of friction 133\dfrac{1}{3\sqrt{3}}. The critical force to be applied on the vertical surface as shown at an angle 60∘60^{\circ} with horizontal such that it does not move, will be 3x3x. The value of xx will
    [g=10ms−2;sin⁡60∘=32;cos⁡60∘=12]\left[g=10m{s}^{-2};\sin 60^{\circ}=\dfrac{\sqrt{3}}{2};\cos 60^{\circ}=\dfrac{1}{2}\right]
    JEE Main/Numerical/Medium/Frictional force/With diagram
  167. 167An inclined plane is bent in such a way that the vertical cross-section is given by y=x24y=\dfrac{{x}^{2}}{4} where yy is in vertical and xx in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ=0.5,\mu =0.5, the maximum height in cmcm at which a stationary block will not slip downward is________cm.cm.JEE Main/Numerical/Medium/Frictional force
  168. 168The coefficient of static friction between a wooden block of mass 0.5kg0.5kg and a vertical rough wall is 0.2.0.2. The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be______NN. ⌈g=10ms−2]\left⌈g=10m{s}^{-2}\right]JEE Main/Numerical/Medium/Frictional force
  169. 169An insect is at the bottom of a hemispherical ditch of radius 1m1m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75,0.75, then hhis :(g=10ms−2):\left(g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/Frictional force
  170. 170A block starts moving up an inclined plane of inclination 30∘30^{\circ} with an initial velocity ofv0{v}_{0}. It comes back to its initial position with velocity v02.\dfrac{{v}_{0}}{2}. The value of the coefficient of kinetic friction between the block and the inclined plane is close to 11000,\dfrac{1}{1000}, The nearest integer to II is :JEE Main/Numerical/Medium/Frictional force
  171. 171A small block starts slipping down from a point BB on an inclined plane ABAB, which is making an angle θ\theta with the horizontal section BCBC is smooth and the remaining section CACA is rough with a coefficient of friction μ\mu. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC=2ACBC=2AC, the coefficient of friction is given by μ=ktanθ\mu =ktan\theta. The value of kk is .......
    JEE Main/Numerical/Medium/Frictional force/With diagram
  172. 172

    Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force     FF at a point bb above its centre of mass (see figure). If the coefficient of friction is μ=0.4\mu =0.4 , the maximum possible value of 100×ba100\times \dfrac{b}{a} for a box not to topple before moving is ________    JEE Main/Numerical/Medium/Frictional force/With diagram
  173. 173A 60HP60HP electric motor lifts an elevator having a maximum total load capacity of 2000kg.2000kg. If the frictional force on the elevator is 4000N,4000N, the speed of the elevator at full load is close to : (1HP=746W,g=10ms−2)\left(1HP=746W,g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/Frictional force
  174. 174Two blocks AA and BB of masses mA=1kg{m}_{A}=1kg and mB=3kg{m}_{B}=3kg are kept on the table as shown in figure. The coefficients of friction between AA and BB is 0.20.2 and between BB and the surface of the table is also 0.2.0.2. The maximum force FF that can be applied on BB horizontally, so that the block AA does not slide over the block BB is : [Take g=10m/s2g=10m/{s}^{2} ]
    JEE Main/MCQ/Medium/Frictional force/With diagram
  175. 175A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N.10N. The coefficient of static friction between the block and the plane is: [Take g=10m/s2g=10m/{s}^{2} ]

    JEE Main/MCQ/Medium/Frictional force/With diagram
  176. 176A body of mass 2 kg2 \mathrm{~kg} slides down with an acceleration of 3 m/s23 \mathrm{~m} / \mathrm{s}^2 on a rough inclined plane having a slope of 30∘30^{\circ}. The external force required to take the same body up the plane with the same acceleration will be: (g=10 m/s2)\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)JEE Main/MCQ/Medium/Frictional force
  177. 177A given object takes nn times more time to slide down a 45o{45}^{o} rough inclined plane as it takes to slide down a perfectly smooth 45o{45}^{o} incline. The coefficient of kinetic friction between the object and the incline is:JEE Main/MCQ/Medium/Frictional force
  178. 178A given object takes nn times more time to slide down a 45∘45^{\circ} rough inclined plane as it takes to slide down a perfectly smooth 45∘45^{\circ} incline. The coefficient of kinetic friction between the object and the incline is :JEE Main/MCQ/Medium/Frictional force
  179. 179Two masses m1=5kg{m}_{1}=5kg and m2=10kg{m}_{2}=10kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.150.15. The minimum weight m that should be put on top of m2{m}_{2} to stop the motion is:

    JEE Main/MCQ/Medium/Frictional force/With diagram
  180. 180A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle θ\theta with the horizontal, a point object of mass m is kept. The minimum coefficient of friction μmin{\mu }_{min} between the mass and the inclined surface such that the mass does not move is:JEE Main/MCQ/Medium/Frictional force
  181. 181A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ\mu . The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR.
    The values of the coefficient of friction     μ\mu and the distance x=(QR)x=\left(QR\right) , are respectively close to:

    JEE Main/MCQ/Medium/Frictional force/With diagram
  182. 182

    Given in the figure are two blocks     AA and BB of weight 20N20N and 100N100N, respectively. These are being pressed against a wall by a force FF and kept in equilibrium as shown. If the coefficient of friction between the blocks is 0.10.1 and between block BB and the wall is 0.150.15, the frictional force applied by the wall on block BB is:    JEE Main/MCQ/Medium/Frictional force/With diagram
  183. 183A heavy box is to be dragged along a rough horizontal floor. To do so, the person AA pushes it at an angle 30∘30^{\circ} from the horizontal and requires a minimum force FA{F}_{A}, while the person BB pulls the box at an angle 60∘60^{\circ} from the horizontal and needs minimum force FB{F}_{B}. If the coefficient of friction between the box and the floor is 35\dfrac{\sqrt{3}}{5}, the ratio FAFB\dfrac{{F}_{A}}{{F}_{B}} isJEE Main/MCQ/Medium/Frictional force
  184. 184A bullet of mass 4 g4 \mathrm{~g} is fired horizontally with a speed of 300 m/s300 \mathrm{~m} / \mathrm{s} into 0.8 kg0.8 \mathrm{~kg} block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.30.3, how far will the block slide approximately?JEE Main/MCQ/Medium/Frictional force
  185. 185A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be :JEE Main/MCQ/Medium/Frictional force
  186. 186A block of mass mm is placed on a surface with a vertical cross section given by y=x36y=\dfrac{{x}^{3}}{6}. If the coefficient of friction is 0.50.5, the maximum height above the ground at which the block can be placed without slipping isJEE Main/MCQ/Medium/Frictional force
  187. 187A body starts from rest on a long inclined plane of slope 45∘45^{\circ}. The coefficient of friction between the body and the plane varies as μ=0.3x\mu=0.3 x, where xx is distance travelled down the plane. The body will have maximum speed (for g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2 ) when x=x=JEE Main/MCQ/Medium/Frictional force
  188. 188A block of weight WW rests on a horizontal floor with coefficient of static friction μ\mu. It is desired to make the block move by applying minimum amount of force. The angle θ\theta from the horizontal at which the force should be applied and magnitude of the force FF are respectively.JEE Main/MCQ/Medium/Frictional force
  189. 189An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/31 / 3. If the line joining the centre of the hemispherical surface to the insect makes an angle α\alpha with the vertical, the maximum possible value of α\alpha so that the insect does not slip is given by
    JEE Main/MCQ/Medium/Frictional force/With diagram
  190. 190Consider a car moving on a straight road with a speed of 100 m/s100 \mathrm{~m} / \mathrm{s}. The distance at which car can be stopped is [μk=0.5]\left[\mu_{\mathrm{k}}=0.5\right]JEE Main/MCQ/Medium/Frictional force
  191. 191The upper half of an inclined plane with inclination ϕ\phi is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given byJEE Main/MCQ/Medium/Frictional force
  192. 192A smooth block is released at rest on a 45∘45^{\circ} incline and then slides a distance d. The time taken to slide is n\mathrm{n} times as much to slide on rough incline than on a smooth incline. The coefficient of friction isJEE Main/MCQ/Medium/Frictional force
  193. 193A block rests on a rough inclined plane making an angle of 30∘30^{\circ} with the horizontal. The coefficient of static friction between the block and the plane is 0.80.8. If the frictional force on the block is 10 N10 \mathrm{~N}, the mass of the block (in kg\mathrm{kg} ) is (take g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )JEE Main/MCQ/Medium/Frictional force
  194. 194A marble block of mass 2 kg2 \mathrm{~kg} lying on ice when given a velocity of 6 m/s6 \mathrm{~m} / \mathrm{s} is stopped by friction in 10 s10 \mathrm{~s}. Then the coefficient of friction isJEE Main/MCQ/Medium/Frictional force
  195. 195A horizontal force of 10 N10 \mathrm{~N} is necessary to just hold a block stationary against a wall. The co-efficient of friction between the block and the wall is 0.20.2. The weight of the block is
    JEE Main/MCQ/Medium/Frictional force/With diagram
  196. 196The minimum velocity (in ms−1\mathrm{ms}^{-1} ) with which a car driver must traverse a flat curve of radius 150 m150 \mathrm{~m} and coefficient of friction 0.60.6 to avoid skidding isJEE Main/MCQ/Medium/Frictional force
  197. 197A car of mass ' mm ' moves on a banked road having radius ' rr ' and banking angle θ\theta. To avoid slipping from banked road, the maximum permissible speed of the car is v0v_0. The coefficient of friction μ\mu between the wheels of the car and the banked road isJEE Main/MCQ/Medium/Non-uniform Circular Motion
  198. 198A car of 800 kg800 \mathrm{~kg} is taking turn on a banked road of radius 300 m300 \mathrm{~m} and angle of banking 30∘30^{\circ}. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: (g=10 m/s2,3=1.73)\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)JEE Main/MCQ/Medium/Non-uniform Circular Motion
  199. 199A particle is moving in a circle of radius 50cm50cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t=0t=0 is 4ms−14m{s}^{-1}, the time taken to complete the first revolution will be 1α[1−e−2π]s\dfrac{1}{\alpha }\left[1-{e}^{-2\pi }\right]s, where α=\alpha =______.JEE Main/Numerical/Medium/Non-uniform Circular Motion
  200. 200A train is moving with a speed of 12ms−112m{s}^{-1} on rails which are 1.5m1.5m apart. To negotiate a curve radius 400m400m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=g= 10ms−210m{s}^{-2}):JEE Main/MCQ/Medium/Non-uniform Circular Motion
  201. 201A car is moving on a horizontal curved road with radius 50m50m. The approximate maximum speed of car will be, if friction between tyres and road is 0.340.34. [Take g=10ms−2g=10m{s}^{-2}]JEE Main/MCQ/Medium/Non-uniform Circular Motion
  202. 202A tube of length 50cm50cm is filled completely with an incompressible liquid of mass 250g250g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity xFrads−1x\sqrt{F}rad{s}^{-1}. If FF be the force exerted by the liquid at the other end then the value of xx will be _____ .JEE Main/Numerical/Medium/Non-uniform Circular Motion
  203. 203A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass mm moves against the wall with a speed vv. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N)\left(N\right) and speed of the block (v)\left(v\right)?
    JEE Main/MCQ/Medium/Non-uniform Circular Motion/With diagram
  204. 204A ball is released from rest from point PP of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point QQ is AA while angular position of point QQ is α\alpha with respect to point PP. Which of the following graphs represent the correct relation between AA and α\alpha when ball goes from QQ to RR?
    JEE Main/MCQ/Medium/Non-uniform Circular Motion/With diagram
  205. 205A curved in a level road has a radius 75m75m. The maximum speed of a car turning this curved road can be 30ms−130m{s}^{-1} without skidding. If radius of curved road is changed to 48m48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____ ms−1m{s}^{-1}.JEE Main/Numerical/Medium/Non-uniform Circular Motion
  206. 206The normal reaction NN for a vehicle of 800kg800kg mass, negotiating a turn on a 30∘30^{\circ} banked road at maximum possible speed without skidding is ____ ×103kgms−2\times {10}^{3}kgm{s}^{-2}.JEE Main/MCQ/Medium/Non-uniform Circular Motion
  207. 207Statement I: A cyclist is moving on an unbanked road with a speed of 7kmh−17km{h}^{-1} and takes a sharp circular turn along a path of the radius of 2m2m without reducing the speed. The static friction coefficient is 0.20.2. The cyclist will not slip and pass the curve (g=9.8ms−2)\left(g=9.8m{s}^{-2}\right)
    Statement II : If the road is banked at an angle of     45∘45^{\circ}, cyclist can cross the curve of 2m2m radius with the speed of 18.5kmh−118.5km{h}^{-1} without slipping. In the light of the above statements, choose the correct answer from the options given below.    JEE Main/MCQ/Medium/Non-uniform Circular Motion
  208. 208A disc rotates about its axis of symmetry in a hoizontal plane at a steady rate of 3.53.5 revolutions per second. A coin placed at a distance of 1.25 cm1.25 \mathrm{~cm} from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is (g=10 m/s2)\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)JEE Main/MCQ/Medium/Non-uniform Circular Motion
  209. 209Two point masses of mass m1=fMm_1=f M and m2=(1−f)M(f<1)m_2=(1-f) M(f \lt 1) are in outer space (far from gravitational influence of other objects) at a distance RR from each other. They move in circular orbits about their centre of mass with angular velocities ω1\omega_1 for m1m_1 and ω2\omega_2 for m2m_2. In that caseJEE Main/MCQ/Medium/Non-uniform Circular Motion
  210. 210A bead of weight ww can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle θ\theta with the vertical then tension of the thread and reaction of the wire on the bead areJEE Main/MCQ/Medium/Non-uniform Circular Motion

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