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Question

The cylinders P and Q are of equal of mas and length but made of metals with densities ρP and ρQ(ρP>ρQ). If their moment of inertia about an axis passing through centre and normal to the circular face be IP and IQ, then:

A
IP=IQ
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B
IP>IQ
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C
IP<IQ
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D
IPIQ
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Solution

The correct option is C IP<IQ
Given: The cylinders P and Q are of equal of mas and length but made of metals with densities ρP and ρQ(ρP>ρQ). If their moment of inertia about an axis passing through centre and normal to the circular face be IP and IQ,
To find the relation between IP and IQ
Solution:
Let mass be m,
We know, m=ρV (as mass=density×volume)
m=ρ×πr2lr2=mπρl.......(i)
Moment of inertia about given axis is,
I=12mr2=12m×mπρlI=m22πρlI1ρIPIQ=ρQρP
Given,
ρP>ρQIP<IQ

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