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Q.

A circular disc of radius R and thickness (R/6) has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter on axis of rotation is

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a

I

b

2I8

c

I5

d

I10

answer is C.

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Detailed Solution

When the disc is melted and recasted into a solid sphere, then,Volume of disc = Volume of the sphereπR2×(R/6)=(4/3)πr3∴r=R/2Now, I=MR22 (Fordisc) I′=25MR2 (For sphere) ∴ I′=25M×R22=12MR2×15or , I′=I/5
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