A disc having radius 1 m is held in contact with ceiling. A light rope is tied at circumference of disc and kept the point at same level as centre the other end of rope is tied at ceiling at $(\sqrt{3} + 1) m$ distance from contact point disc is released from rest. The rope length is $\sqrt{7} m .$ The rope snaps due to impulse and disc momentarily moves horizontally, just after snapping. The angular velocity of disc after snapping is $k \sqrt{20}$ rad/s. Find the value of k. $(g = 10 m / s^{2})$

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Detailed Solution

Impulse equation
Question Image
$J \cos θ = m \sqrt{2 g R}$
Angular impulse equation
$J \cos θ R = \frac{m R^{2}}{2} ω$
$ω = 2 \sqrt{20}$

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