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Question

The moment of inertia of a solid sphere about an axis passing through its centre is 0.4 kg-m2. If mass of the sphere is kept same, but its density is increased eight times, find the new moment of inertia of the sphere about the same axis.

A
0.4 kg-m2
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B
0.1 kg-m2
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C
0.3 kg-m2
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D
0.2 kg-m2
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Solution

The correct option is B 0.1 kg-m2
We know,
Density(ρ)= Mass(M)Volume(V)
Volume(V)=4πr33
If density is increased 8 times and mass is kept same,
New density, ρ=8×ρ
MV=8×MV
V=V8
4πr33=18×4πr33
r=r2 (new radius)
We know moment of inertia of solid sphere about an axis passing through its C.O.M
I=25Mr2
New MOI, I=25Mr2

II=r2r2=14

I=I4=0.44=0.1 kg-m2

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