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 B0.1 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 ⇒4πr′33=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′=25Mr′2