Question

Assertion (A): IS and IH 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}}. $ Reason (R): 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 A and R are true and R is the correct explanation of A
• B. both A and R are true and R is not correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

Answer: (A)

The moment of inertia of solid sphere about its diameter $ {{I}_{S}}=\frac{2}{5}M{{R}^{2}} $ The moment of inertra of a thin walled hollow sphere about its diameter is $ {{I}_{H}}=\frac{2}{5}M\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})} $ where $ {{R}_{1}} $ and $ {{R}_{2}} $ are its internal and external radii $ {{I}_{S}}>{{I}_{H}} $ The reason is that in solid sphere the whole mass is uniformly and continuously distributed about its centre in the whole volume while in hollow sphere the mass is distributed on the surface of sphere.