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A smooth rod OP is fixed vertically. A disc of mass m and radius R is rolling without slipping on a rough horizontal surface as shown. Velocity of centre of mass of disc is $v_{0}$ . A rod AB of length L is connected with disc at A, R/2 distance vertically up from centre of disc with pin joint (about which it can rotate freely), other end of the rod is attached to a small smooth ring B, which can move freely over rod OP. At an instant rod AB makes an angle $60^{0}$ with the vertical. The velocity of ring on the vertical rod at this instant is

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$\frac{3 \sqrt{3}}{2} v_{0}$

$\frac{v_{0}}{2}$

$\frac{3}{2} v_{0}$

$v_{0}$

answer is A.

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Detailed Solution

$v \cos 60^{0} = \frac{3 v_{0}}{2} \cos 30^{0}, v = \frac{3 \sqrt{3}}{2} v_{0}$

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