A disc of mass 2 kg and radius 0.2 m is rotating with an angular velocity of 30 rad s - 1 . The angular velocity of the disc, if a mass of 0.25 kg is put on the periphery is

Step-by-step solution

If no external torque acts on a system of particle then angular momentum of the system remains constant, that is, τ = 0 ⇒ dL dt = 0 ⇒ L = Iω = constant ⇒ I 1 ω 1 = I 2 ω 2 ∴ 1 2 Mr 2 ω 1 = 1 2 M + 2 m r 2 ω 2 ...(i) Here, M = 2   kg , m = 0.25   kg and r = 0.2   m ω 1 = 30   rad   s - 1 Hence, we get after putting the given values in Eq. (i) 1 2 × 2 × 0.2 2 × 30 = 1 2 × 2 + 2 × 0.25 0.2 2 × ω 2 &#8