Question

Two rings of radius \( R \) and \( nR \) made of same material have the ratio of moment of inertia about an axis passing through the centre is 1 : 8. The value of \( n \) is a

• A. 2
• B. \( \sqrt{2} \)
• C. 4
• D. \( \frac{1}{2} \)

Hint:

The moment of inertia of a ring is proportional to the square of its radius.

Answer 1

The Correct Option is A

Step 1: Use the formula for the moment of inertia of a ring.
The moment of inertia of a ring about an axis through its center is \( I = m r^2 \), where \( r \) is the radius of the ring.
Step 2: Set up the equation for the ratio of moments of inertia.
For the two rings, the ratio of their moments of inertia is given by: \[ \frac{I_2}{I_1} = \frac{m (nR)^2}{m R^2} = n^2 \] Given the ratio is 8, we find \( n = 2 \). Final Answer: \[ \boxed{2} \]