The moment of inertia of a disc of mass M and radius R about any diameter is MR²/4. Its moment of inertia about an axis normal to the disc and passing through a point on its edge is (x/2)MR². Find x.
Physics · Rotational Motion · Moment of Inertia & Rotational Kinetic Energy
JEE Mains 1st Feb Evening Shit 2023

Question

The moment of inertia of a disc of mass M and radius R about any diameter is MR²/4. Its moment of inertia about an axis normal to the disc and passing through a point on its edge is (x/2)MR². Find x.

Physics · Rotational Motion · Moment of Inertia & Rotational Kinetic Energy

JEE Mains 1st Feb Evening Shit 2023

G1 Physics · Accepted Answer

Moment of inertia about the central axis normal to the disc: I꜀ₘ = MR²/2 Using the parallel-axis theorem for an axis through the edge: I = I꜀ₘ + MR² = MR²/2 + MR² = 3MR²/2 Comparing with: I = (x/2)MR² gives x = 3.