A circular hole of radius R 4 is made in a thin uniform disc having mass and radius R , as shown in figure.…

A circular hole of radius R4 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-
  1. 219MR2256
  2. 237MR2512
  3. 197MR2256
  4. 19MR2512

Solution

ID=mr22

Moment of inertia of removed portion about the axis.

Iremoved=12  m16  r216+m16  9r216   (by parallel axis theorem)

=mr2+18mr2512

=19mr2512

Iremaining=mr22-19512 mr2

=237512 mr2

Asked in: JEE Main 2017 (09 Apr Online)

Practice more Rotational Motion questions on Aicharya