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Question

The surface mass density of a disc of radius a varies with radial distance r as σ=A+Br where A & B are positive constants. Then, moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane (in kg m2) is:

A
2πa4(A4+Ba5)
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B
2πa4(Aa4+B5)
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C
πa4(A4+Ba5)
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D
2πa4(A5+Ba4)
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Solution

The correct option is A 2πa4(A4+Ba5)

Given, σ=A+Br
Then, total mass of disc =a0dm=a0(A+Br)2πrdr
Moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane is
I=a0dmr2
=a0(A+Br)2πr3dr
=2π(Aa44+Ba55)
=2πa4(A4+Ba5)
Thus, option (a) is the correct answer.

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