A disc of mass 2 kg and radius 0 . 2 m is rotating with an angular velocity 30 rad s - 1 , about an axis passing through its centre and perpendicular to its plane. If a mass of 0 .25 kg is stuck on the periphery of the disc, then its angular velocity will become

Step-by-step solution

When there is no external torque then the angular momentum remains constant. i.e. τ = 0 ⇒ d L d t = 0 ∴       I 1 ω 1 = I 2 ω 2 ... (i) Here M = 2   kg ,   m = 0.25   kg ,   r = 0.2   m , ω 1 = 30   rad   s - 1 Hence, putting the value of ω 1 in equation (i), we get ⇒       1 2 × 2 × 0.2 2 × 30 = 1 2 × 2 + 2 × 0.25 0.2 2 × ω 2 ⇒       1.2 = 0.05 ω 2