Question

The moment of inertia of a ring about one of its diameter is $I$. What will be its moment of inertia about a tangent parallel to the diameter?

• A. $44$
• B. $2I$
• C. $\frac{3}{2}I$
• D. $3I$

Answer 1

Answer: (D)

$3I$

The moment of inertia of a ring about of its diameter is given by $I_{dia}=I=\frac{1}{2}M{R}^2$ where $R=$ radius of ring.

Here, the distance between the tangent and the diameter is $R$.

By parallel axis theorem, the moment of inertia about the tangent is

$I_T=I_{dia}+M{R}^2=I+2I=3I$ (as $M{R}^2=2I$)