Question

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $ {{I}_{A}} $ and $ {{I}_{B}} $ such that

• A. $ {{I}_{A}}={{I}_{B}} $
• B. $ {{I}_{A}}>{{I}_{B}} $
• C. $ {{I}_{A}}<{{I}_{B}} $
• D. $ \frac{{{I}_{A}}}{{{I}_{B}}}=\frac{{{d}_{A}}}{{{d}_{B}}} $

Answer 1

Answer: (C)

Let same mass and same outer radii of solid Sphere and hollow sphere are M and R respectively. The moment of inertia of solid sphere A about its diameter $ {{I}_{A}}=\frac{2}{5}M{{R}^{2}} $ ...(i) Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter $ {{I}_{B}}=\frac{2}{3}M{{R}^{2}} $ ...(ii) It is clear from Eqs, (i) and (ii), $ {{I}_{A}}<{{I}_{B}} $ is. where $ {{d}_{A}} $ and $ {{d}_{B}} $ are their densities.