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Question:

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is IO and IP, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio IP/IO to the nearest integer is:

3713

7331

813

1337

Solution:

IP = [4mR2/2 + 4mR2] - [mR2/8 + 5mR2/4] (by the method of superposition of moment of inertia)
IP = 37mR2/8 (1)
IO = [4mR2/2] - [mR2/8 + mR2/4]
IO = 13mR2/8.. (2)
So, IP/IO = 37/13
Approximately 3