Question

Which option is correct if $I_{1},I_{2}$ and $I_{3}$ are moments of inertia of solid sphere, hollow sphere and a ring of same mass and radius,

• A. $I_{1}>I_{2}>I_{3}$
• B. $I_{3}>I_{2}>I_{1}$
• C. $I_{2}>I_{1}>I_{3}$
• D. $I_{2}>I_{3}>I_{1}$

Answer 1

Answer: (B)

Let $m$ be the mass and $r$ be the radius of the bodies, then the moment of inertia of solid sphere will be,
$I_{1}=\frac{2}{5}mr^{2}$
The moment of inertia of hollow sphere will be,
$I_{2}=\frac{2}{3}mr^{2}$
The moment of inertia of the ring is given by,
$I_{3}=mr^{2}$
Therefore, $I_{3}>I_{2}>I_{1}$ .