Question

A block of mass $M$ with the 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 the top, the distance moved by block when the cylinder reaches the bottom of the track is

• A. $R-r$
• B. $\frac{m \left(R - r\right)}{M + m}$
• C. $\frac{M}{M + m} \, \left(R - \, r\right)$
• D. $\frac{M}{M - m} \, r$

Answer 1

Answer: (B)

COM of system $\left(B l o c k \, + \, c y l i n d e r\right)$ remains at rest. If $x$ is the distance moved by block when cylinder moves from top to bottom $\left(M \, + \, m\right) \, x=m \, \left(R - r\right)$
$X=\frac{m \left(R - r\right)}{M + m}$