Question

$I_S$ and $I_H$ are the moments of inertia about the diameters of a solid and thin walled hollow sphere respectively. If the radii and the masses of the above spheres are equal, $I_H > I_S$. In solid sphere, the mass is continuously and regularly distributed about the centre whereas the mass, to a large extent, is concentrated on the surface of hollow sphere

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false
• D. Both assertion and reason are false

Answer 1

The Correct Option is A

The moment of inertia of solid sphere about its diameter
$I_S=\frac{2}{3}MR^2$
The moment of inertia of a thin walled hollow sphere about its diameter is
$I_H=\frac{2}{5}M\frac{(R^5_2-R^5_1)}{(R^3_2-R^3_1)}$ where $R_1 \,and \,R_2$ are its internal and external radii
= $I_H >I_s$
The reason is that in solid sphere the whole mass is uniformly and continuously distributed about its center in the whole volume while in hollow sphere the mass is distributed on the surface of sphere