Question

A block of mass $M$ with a semicircular track of radius $R$ rests on a horizontal frictionless surface. A uniform cylinder of radius $r$ and mass $m$ is released from rest from the top point $A$. The cylinder steps on the semicircular frictionless track. The distance travelled by the block when the cylinder reaches the point $B$ is :

• A. $\frac{M(R-r)}{M+m}$
• B. $\frac{m(R-r)}{M+m}$
• C. $\frac{(M+m)R}{M}$
• D. None of the above

Answer 1

The correct option is B $\frac{m(R-r)}{M+m}$

Here we are using the concept of center of mass.

Let block $m$ move left and cylinder of mass $m$ move $(R-r-x)$ right.

Now let center of mass and origin be,

$X_{cm}=\frac{m(R-r-x)-xM}{m+M}=0$

$=m(R-r)-mx=xM=0$

That is,

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