Question bank/JEE Main/Physics

JEE MainPhysicsModerateWork Power & Energy

Two children are playing a game in which they try to hit a small
box using a spring-loaded marble gun, which is fixed rigidly to a table
is a height h above the top of the box. The spring has a spring constant
k and the edge of the box is some unknown horizontal distance
l\mathcal{l} away from the table. The first child compresses the spring
a distance x and finds that the marble falls short of its target by a
horizontal distance y. The second child compresses the spring by an
extra amount Δx\Delta x so that marble lands in the box. The value of
Δx\Delta xis ymgNhky\sqrt{\frac{mg}{Nhk}} (Where N is integer) then find the
value of N.

Show answer and solution
time taken or time of flight is same for both projectiles.
i.e. t=2hgt = \sqrt{\frac{2h}{g}}
using energy conservation:
⇒12kx2=12mv2\Rightarrow \frac{1}{2}{kx}^{2} = \frac{1}{2}{mv}^{2}.......(1)
⇒12k(x+Δx)2=12mv′2\Rightarrow \frac{1}{2}k(x + \Delta x)^{2} = \frac{1}{2}mv^{'2}.......(2)
l−y=vt\mathcal{l -}y = vt.......(3)
l=v′t\mathcal{l =}v't.......(4)
On solving we get
Δx=ymg2hk\Delta x = y\sqrt{\frac{mg}{2hk}}
N = 2

Source: Grass-G / P-16 Physics paper 25 Nov First.docx

More JEE Main questionsChapter practice

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.

Scan a doubtView plans