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Question: A block of mass M with semicircular track of radius R rests on a horizontal smooth surface. A cylind...

A block of mass M with semicircular track of radius R rests on a horizontal smooth surface. A cylinder of radius r slips on the track. If the cylinder is released from rest from top, the distance moved by block when cylinder reaches the bottom of the track is

A

R – r

B

M(R−r)M+m\frac { \mathrm { M } ( \mathrm { R } - \mathrm { r } ) } { \mathrm { M } + \mathrm { m } }

C

MM+m(R−r)\frac { M } { M + m } ( R - r )

D

MM−m\frac { M } { M - m } r

Answer

M(R−r)M+m\frac { \mathrm { M } ( \mathrm { R } - \mathrm { r } ) } { \mathrm { M } + \mathrm { m } }

Explanation

Solution

Let x be the distance moved by the block when cylinder moves from top to the bottom.

Here (M + m)x = m(R - r)

or x = m(R−r)M+m\frac { m ( R - r ) } { M + m }