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 I5given radius of the disc =Rthickness of the disc = R6volume of the disc V1=πR2t=πR2R6=πR36let the radius of the sphere be R′volume of the sphere V2=43πR′3since volume remains sameπR36=43πR′3⟹R3=8(R′)3⟹R=2R′let I1 be the M.O.I of disc =MR22let I2 be M.O.I of the sphere = 25M(R′)2=25M(R2)2I2=I1(15)

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