Skip to content
dronacharya.ai
← JEE Advanced 2014 · Paper 1
PhysicsInteger+3Question 18 of 60

JEE Advanced 2014 · Paper 1, Physics question 18

A rocket is moving in a gravity free space with a constant acceleration of 2 m s−22\ \mathrm{m\,s^{-2}} along +x+x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x+x direction with a speed of 0.3 m s−10.3\ \mathrm{m\,s^{-1}} relative to the rocket. At the same time, another ball is thrown in −x-x direction with a speed of 0.2 m s−10.2\ \mathrm{m\,s^{-1}} from its right end relative to the rocket. The time in seconds when the two balls hit each other is

A 4 m long chamber accelerating at a = 2 m s⁻² in +x; a ball at the left end moves right at 0.3 m s⁻¹ and a ball at the right end moves left at 0.2 m s⁻¹ (relative to the rocket).
Answer and worked solution

Official answer: 2

In the rocket's frame both balls have the same acceleration, 2 m s−22\ \mathrm{m\,s^{-2}} in the −x-x direction (pseudo-force). Their relative acceleration is zero.

Ignoring the walls. The relative speed is 0.3+0.2=0.5 m s−10.3+0.2=0.5\ \mathrm{m\,s^{-1}} over 4 m:
t=40.5=8 s.t=\frac4{0.5}=8\text{ s}.

Allowing for the left wall. The first ball's position is x1=0.3t−t2x_1=0.3t-t^2, which returns to the left wall at t=0.15t=0.15 s. If it then stays at the wall, the second ball reaches it when 4−0.2t−t2=04-0.2t-t^2=0, at t≈1.9≈2t\approx1.9\approx2 s.

The question does not say what happens at the wall, so the official key accepts both readings.

Answer: 8 (key: 2 or 8)

Topics:Pseudo forces and non-inertial framesMotion in a straight line
← Previous questionNext question →