JEE Main202522 Jan 2025Morning ShiftPhysicsRotational MotionActual
A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R / 2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
Options
- A7 32 MR ^2
- B9 32 MR ^2
- C17 32 MR ^2
- D13 32 MR ^2
Correct answer
D. 13 32 MR ^2
Step-by-step solution
aligned & I_ complete = M R^2 2 & aligned I_ removed & = ( M 4 ) ( R 2 )^2 1 2 + ( M 4 ) ( R 2 )^2 & = 3 M R^2 32 I= M R^2 2 & - 3 M R^2 32 = 13 32 M R^2 aligned aligned