Question

A small box starts sliding from rest at the top of the frictionless track of radius $R$. The initial height of the box equal to $2R$ above a horizontal surface. At the moment, the box leaves the bottom of the track, a ball of the same mass as the box is dropped from the same height at the bottom of the track.
Once the box leaves the bottom of the slide, which of the following statements best describes the motions of the box and the ball?

• A. The ball hits the floor at the same time as the box
• B. The ball hits the floor before the box does
• C. The ball hits the floor after the box does
• D. The acceleration of the box is greater than the acceleration of the ball
• E. The acceleration of the ball is greater than the acceleration of the box

Answer 1

Answer: (A)

The ball hits the floor at the same time as the box

As box and ball are falling freely from same height so they would have same acceleration $g$ and due to this they will hit the floor at the same time ,

It can be understood by equation $h=ut+\frac{1}{2}g{t}^2$

Given $u=0$, since height and acceleration are same for both, time would also be same.