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. $\frac{R}{2}$
• B. $\frac{R}{4}$
• C. $\frac{R}{2}$ $\sqrt{2}$
  
• D. $\frac{R}{\sqrt{2}}$

Answer 1

The correct option is B

$\frac{R}{4}$

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 = $\frac{x}{2}$ = $\frac{R}{4}$