Question

One solid sphere $A$and another hollow sphere $B$ are of the same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_A$​ and $I_B$ such that (where $d_A$ and $d_B$ are their densities)

• 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

The correct option is C

$I_A<I_B$

Step 1. Given data:

Mass of both spheres = $M_A=M_B=M$

Radii of both spheres= $R_A=R_B=R$

Step 2. Calculations:

We know, moment of inertia of a solid sphere is given by, $I_A=\frac{2}{5}{M}_A{R_A}^2=\frac{2}{5}M{R}^2$

Also, moment of inertia of a hollow sphere is given by, $I_B=\frac{2}{3}{M}_B{R_B}^2=\frac{2}{3}M{R}^2$

Hence, as evident from above, $I_A<I_B$

Thus, the correct option is option C.