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Statement I: A cyclist is moving on an unbanked road with a speed of 7kmh^-1 and takes a sharp circular turn along a path of the radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve (g=9.8ms^-2 ) Statement II : If the road is banked at an angle of 45^°, cyclist can cross the curve of 2m radius with the speed of 18.5kmh^-1 without slipping. In the light of the above statements, choose the correct answer from the options given below.

Statement I is incorrect and statement II is correct

Statement I is correct and statement II is incorrect

Both statement I and statement II are false

Laws of Motion

JEE Main level, single correct, medium

207 of 210

Question 207 of 210

Statement I: A cyclist is moving on an unbanked road with a speed of $7km{h}^{-1}$ and takes a sharp circular turn along a path of the radius of $2m$ without reducing the speed. The static friction coefficient is $0.2$ . The cyclist will not slip and pass the curve $\left(g=9.8m{s}^{-2}\right)$
Statement II : If the road is banked at an angle of $45^{\circ}$ , cyclist can cross the curve of $2m$ radius with the speed of $18.5km{h}^{-1}$ without slipping. In the light of the above statements, choose the correct answer from the options given below.

Show answer and solution

Answer: (D) Both statement I and statement II are true

Statement I

{v}_{\max }=\sqrt{\mu Rg}=\sqrt{\left(0.2\right)\times 2\times 9.8}

{v}_{\max }=1.97m{s}^{-1}

7km{h}^{-1}=1.944m{s}^{-1}

Speed is lower than

{v}_{\max }

, hence it can take safe
turn.
Statement II

{v}_{\max }=\sqrt{Rg\left[\dfrac{tan\theta +\mu }{1-\mu tan\theta }\right]}

=\sqrt{2\times 9.8\left[\dfrac{1+0.2}{1-0.2}\right]}=5.42m{s}^{-1}

18.5km{h}^{-1}=5.14m{s}^{-1}

Speed is lower than

{v}_{\max }

, hence it can take safe turn.

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