Q. One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radius. Their moments 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}}\ $
Explanation
(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
$I_{A} = \frac{2}{5}MR^{2}$ ...(i)
Similarly, the moment of inertia of hollow sphere (spherical shell) $B$ about its diameter
$I_{B} = \frac{2}{3}MR^{2}$ …(ii)
It is clear from Eqs. (i) and (ii), we get
$I_{A} < I_{B}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.