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Question

A circular disc of radius R and thickness R/6 has moment of inertia I about an axis passing through its center and perpendicular to its plane. It is melt and recast into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is:

A
I5
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B
2I5
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C
4I5
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D
I10
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Solution

The correct option is A I5
given radius of the disc =R
thickness of the disc = R6
volume of the disc V1=πR2t=πR2R6=πR36
let the radius of the sphere be R
volume of the sphere V2=43πR3
since volume remains same
πR36=43πR3R3=8(R)3R=2R
let I1 be the M.O.I of disc =MR22
let I2 be M.O.I of the sphere = 25M(R)2=25M(R2)2
I2=I1(15)


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