Question

The moment of inertia of the disc used in torsional pendulum about the suspension wire is 0.2 kg -m² . It oscillates with a period of 2s. Another disc is played over the first one and the time period of the system becomes 2.5 s. Fine the moment of inertia of the second disc about the wire.

Answer 1

As another disc is placed on the first disc moment of inertia about the axis passing through the wire increases and thus time period increases.

Let the torsional constant of the wire be k. The moment of inertia of the first disc about the wire is 0.2 kg -m². hence, the time period is 

When the second disc having moment of inertia I₁ about. The wire is added, the time period is