A thin circular ring of mass M and radius 'r' is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be -

The objects are placed gently, so no external torque acts about the axis. Use the law of conservation of angular momentum.
Initial moment of inertia of the ring about its axis: $I_1 = Mr^2$
Each of the four objects is at distance r from the axis, so final moment of inertia: $I_2 = Mr^2 + 4mr^2$
$I_1\omega = I_2\omega'$
$Mr^2\omega = (Mr^2 + 4mr^2)\omega'$
$\Rightarrow \omega' = \dfrac{M\omega}{M + 4m}$
The angular velocity decreases because the moment of inertia has increased.