Question

Inside a smooth spherical shell of radius R a ball of the same mass is released from the shown position ( fig. ). Find the distance travelled by the shell on the horizontal floor when the ball comes to the just opposite position of itself with respect to its position in the shell.

• A. $\frac{3R}{5}$
• B. $\frac{R}{4}$
• C. $\frac{3R}{4}$
• D. $\frac{5R}{4}$

Answer 1

The correct option is C $\frac{3R}{4}$

The correct option is C.

Given,

A spherical shell having radius $R$. And a ball is placed inside the spherical shell.

So,

Let the shell travel $x$ distance on the floor.

The ball travels a distance of $(x+0)$ in x-direction with respect to the floor.

So, conserving center of mass is:

$\Rightarrow m\left(\frac{3R}{4}\right)+mx=0$

$\Rightarrow m\left(\frac{3R}{4}\right)=-mx$

$\Rightarrow x=(-\frac{3R}{4})$

Thus, the Ball travels $\frac{3R}{4}$ in the opposite direction.