A uniform disc rotating freely about a vertical axis makes `90` rpm. A small piece of wax of mass `m` gram falls vertically on the disc and sticks to it at a distance `r cm` from the axis. If number of rotations per minute reduces to `60`, find the moment of inertia of the disc.

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. Here are the steps to find the moment of inertia of the disc:

### Step 1: Understand the initial conditions
The disc is initially rotating at 90 revolutions per minute (rpm). We can convert this to radians per second for calculations:
\[ \omega_i = 90 \text{ rpm} = 90 \times \frac{2\pi \text{ radians}}{1 \text{ minute}} = 90 \times \frac{2\pi}{60} \text{ rad/s} = 3\pi \text{ rad/s} \]

...