Question

A uniform solid cylinder of mass $2kg$ and radius $0.2m$ is released from rest at the top of a semicircular track of radius $0.7m$ cut in a block of mass $M=3kg$ as shown in Figure. 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. $0.5m$
• C. $0.7m$
• D. $0.2m$

Answer 1

The correct option is D $0.2m$

Let distance traveled by block is x, towards left.

Displacement of cylinder w.r.t. R is $(R-r)$ towards right.

Therefore, displacement of cylinder w.r.t. ground will be $\left[\right(R-r)-x]$ towards right.

So, $r=0.2m$

$R=0.7m$

$M=3㎏$

$m=2㎏$

$Mx=m(R-r-x)$

$3x=2(0.7-0.2-x)$

$3x=2\left(0.5\right)-2x$

$5x=1$

$\Rightarrow x=0.2m$