A circular hole of radius R 4 is made in a thin uniform disc having mass and radius R , as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is-

Question

A circular hole of radius R 4 is made in a thin uniform disc having mass and radius R , as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is-, 219 M R 2 256, 237 M R 2 512, 197 M R 2 256, 19 M R 2 512

MARKS App · Accepted Answer

I D = m r 2 2 Moment of inertia of removed portion about the axis. I r e m o v e d = 1 2 m 16 r 2 16 + m 16 9 r 2 16 (by parallel axis theorem) = m r 2 + 18 m r 2 512 = 19 m r 2 512 I r e m a i n i n g = m r 2 2 - 19 512 m r 2 = 237 512 m r 2

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