Question

A uniform solid cylinder of mass `2 kg` and radius `0.2 m` is released from rest at the top of a semicircular track of radius `0.7 m` cut in a block of mass `M = 3 kg` as shown in Fig. The block is resting on a smooth horizontal surface and the cylinder rolls down without slipping. Based on the above information, answer the following questions:

The distance moved by the block when the cylinder reaches the bottom of the track is
A. `0.3m`
B. `0.5 m`
C. `0.7m`
D. `0.2m`

Answer 1

Correct Answer - D
As no external force acting force is acting on the system (block `+` cylinder) in the horizontal direction, the linear momentm of the system remains conserved in the horizontal direction.
As the cylinder reachs the bottommost point of the track, its centre of mass covers a horizontal distance of `0.25 m (R-r)` w.r.t block towards the right. Let the block move by `x` in backward direction then
`Mx=m(0.5-x)`
`x=(2xx0.5)/(2+3)=0.2m`