A uniform disc of mass  and radius  is pivoted smoothly at . If a uniform disc of mass  and radius  is welded at the lowest point of the disc, find the period of SHM of the system (disc + ring ).(in seconds)

(2)

The time period of a physical pendulum is

Here we have three quantities  and

Let us calculate the quantities one by one as follows:

Finding

Where

And

Then, we have

Finding

Where

 and

This gives

Finding

Substituting  in the expression

After substituting the values we get