JEE Main 2011 — Rotational Motion Question with Solution

Here no external force is applied on the disc so Torque ($$\tau$$) = 0.

So angular momentum is conserved.

That means $$I_1{\omega }_1=I_2{\omega }_2$$

$$\Rightarrow$$ $${\omega }_2=\frac{I_1{\omega }_1}{I_2}$$

$$\therefore$$ Angular speed is inversely proportional to Moment of inertia.

For disc $$I=\frac{1}{2}M{R}^2$$

$$\therefore$$ Moment of Inertia is proportional to Mass.

As insect moves along a diameter, the effective mass of disc first decreases then increases and hence the moment of inertia first decreases then increases so from principle of conservation of angular momentum, angular speed, first increases then decreases.