Question

Inside a follow sphere of mass M, a rod length $R\sqrt{2}$ is released from the state of rest in the with the orientation shown in figure. The mass of the rod is same as that of the sphere. If inner radius of the hollow sphere is R. then find out its horizontal displacement with respect to earth in the time in which the rod becomes horizontal.

• A. $\frac{R}{2}$
• B. $\frac{R}{4}$
• C. $\frac{R}{2\sqrt{2}}$
• D. None of these

Answer 1

The correct option is A $\frac{R}{2}$

With respect to the axis, Initial position of rod along x-axis is $\frac{-R}{2}$

Let the centers of both rod and circle after rotation becomes horizontal with x.

$\Rightarrow m\left(\frac{-R}{2}\right)+m\left(0\right)=m(-x)+m\left(0\right)$

$\Rightarrow x=\frac{R}{2}.$

Hence, the answer is $\frac{R}{2}.$