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.