Question

A uniform solid cylinder of mass $2kg$ and radius $0.2m$ is released from the rest at the top of a semicircular track of radius $0.7m$ cut in block of mass $M=3kg$ as shown. The block is resting on a smooth horizontal surface and the cylinder rolls down without slipping. The distance moved by the block when the cylinder reaches the bottom of the track is:

• A. $0.3m$
• B. $0.5m$
• C. $0.7m$
• D. $0.2m$

Answer 1

The correct option is D $0.2m$

As there is no external force on the system in horizontal direction $X_{cm} will not change.

$X_{cm}=\frac{\sum M_i{x}_i}{\sum M_i}$

initial $X_{cm}=\frac{3\left(0.7\right)+2\left(0.2\right)}{3+2}=0.5$ $equation$ $1$

Let the distane moved by block be $x$

$X_{cm}=\frac{3(0.7-x)+2(0.7-x)}{3+2}$

using equation 1

$\frac{3(0.7-x)+2(0.7-x)}{5}=0.5$

$x=0.2m$