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. \(I\)
• B. \(\dfrac{2I}{8}\)
• C. \(\dfrac{I}{5}\)
• D. (I)/(10)

Hint:

When bodies are reshaped: Mass conserved ⟹ Volume conserved Always compare MOI using mass relations.

Answer 1

The Correct Option is C

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)