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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When bodies are reshaped:
Mass conserved ⟹ Volume conserved
Always compare MOI using mass relations.
Updated On: Mar 19, 2026
- \(I\)
- \(\dfrac{2I}{8}\)
- \(\dfrac{I}{5}\)
- (I)/(10)
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The Correct Option is C
Solution and Explanation
Step 1: Volume of disc: Vd=π R²((R)/(6))=(π R³)/(6)
Step 2: Let radius of sphere be a: (4)/(3)π a³=(π R³)/(6) ⟹ a=(R)/(2)
Step 3: MOI of disc: Id=(1)/(2)MR²=I
Step 4: MOI of solid sphere about diameter: Iₛ=(2)/(5)Ma²=(2)/(5)M((R)/(2))²=(1)/(10)MR²
Step 5: (Iₛ)/(Id)=(1/10)/(1/2)=(1)/(5) ⟹ Iₛ=(I)/(5)
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