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Question

I is moment of inertia of a uniform circular plate of radius R about its natural axis. If a circular hole of diameter R is made in that plate such that the centre of hole coincides with centre of plate then the moment of inertia of remainder plate about same axis is:

A
I16
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B
15I16
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C
I8
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D
7I8
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Solution

The correct option is B 15I16
Radius of the hole = R/2
Mass corresponding to radius M R2
So, mass corresponding to radius = R/2 M/4
M.I. of remainder of the plate + MI of the hole = MI of the plate
IR+IH=I
IR+M4(R2)2=MR2
IR=1516MR2

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