Question

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

• A.
• B.
• C.
  
• D.

Answer 1

The correct option is B

Let x = displacement of center of mass of rod with respect to sphere along x axis, then,
x = $\frac{\sqrt{2R}}{2}$ cos ${45}^{\circ }$ = $\frac{\sqrt{2R}}{2\sqrt{2}}$ = $\frac{R}{2}$

y = displacement of sphere with respect to ground.
My = M(x - y) $\Rightarrow$ y = $\frac{x}{2}$ = $\frac{R}{4}$