# A Solid Sphere And A Hollow Sphere Of The Same Mass Have The Same Moment Of Inertia About Their Respective Diameters. The Ratio Of Their Radii Will Be(A) 1:2.(B) 5:4. (C) Sqrt 3 : Sqrt 5.(D) Sqrt 5 : Sqrt 3.

We know:

The moment of inertia of solid sphere,$$I_{s} = \frac{2}{5}m_{s}R_{s}^{2}$$

The moment of inertia of hollow sphere,$$I_{H} = \frac{2}{3}m_{H}R_{H}^{2}$$

As given:

$$I_{s} = I_{H} = ?$$ $$\Rightarrow \frac{2}{5}m_{s}R_{s}^{2} = \frac{2}{3}m_{H}R_{H}^{2}$$ $$\Rightarrow \left ( \frac{R}{{R}’} \right ) = \frac{5}{3}$$ $$\Rightarrow \frac{R}{{R}’} =\sqrt{5} :\sqrt{2}$$

Therefore, the ratio of their radii will be $$\sqrt{5} :\sqrt{2}$$

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