Question:
A circular disc of radius R and thickness (R)/(6) has moment of inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is:
A circular disc of radius R and thickness (R)/(6) has moment of inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is:
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Always conserve mass (or volume) when objects are reshaped.
Updated On: Mar 23, 2026
- \(I\)
- \(\dfrac{2I}{8}\)
- \(\dfrac{I}{5}\)
- (I)/(10)
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The Correct Option is D
Solution and Explanation
Step 1: Volume conservation:
\( \pi R^2 \left(\dfrac{R}{6}\right) = \dfrac{4}{3}\pi r^3 \)
\( \Rightarrow r = \dfrac{R}{2} \)
Step 2: Disc moment of inertia:
\( I = \dfrac{1}{2}MR^2 \)
Step 3: Sphere moment of inertia:
\( I_s = \dfrac{2}{5}Mr^2 = \dfrac{2}{5}M\left(\dfrac{R}{2}\right)^2 = \dfrac{MR^2}{10} \)
Step 4: Hence:
\( I_s = \dfrac{I}{5} \)
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