Question

Assertion (A) : $I_S$ and $I_H$ are the moments of inertia about the diameters of a solid sphere and thin walled hollow sphere respectively. If radii and the masses of the above are equal, then $I_H$ > $I_S$
Reason (R) : In a solid sphere, the mass is continuously and regularly distributed about centre, whereas in case of hollow sphere the mass is concentrated on the surface of hollow sphere.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A)
• B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
• C. (A) is true but (B) is false
• D. (A) is false but (B) is true

Answer 1

The correct option is A Both (A) and (R) are true and (R) is the correct explanation of (A)

$I_S=\frac{2}{5}M{r}^2$

$I_H=\frac{2}{3}M{r}^2$

$I_H>I_S.$

The mass of the hollow sphere is concentrated at the surface away from the the axis which increases the distance of mass from the axis and the mass of the solid sphere in concentrated through out the volume, due to which the moment of inertia of hollow sphere is greater than solid sphere.