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

Question

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, 24 rad s - 1, 36 rad s - 1, 15 rad s - 1, 26 rad s - 1

MARKS App · Accepted Answer

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 ⇒ ω 2 = 24 rad s - 1

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