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  4. A smooth rod OP is fixed vertically. A disc of mass m and radius R is rolling without slipping at the given instant on a rough horizontal surface as shown. Velocity of centre of mass C of disc is v0 . 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° with the vertical. The velocity of ring on the vertical rod at this instant is. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-acjdscf0hpak.png />

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Q. A smooth rod $OP$ is fixed vertically. A disc of mass $m$ and radius $R$ is rolling without slipping at the given instant on a rough horizontal surface as shown. Velocity of centre of mass $C$ 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^\circ $ with the vertical. The velocity of ring on the vertical rod at this instant is.

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

Solution
$V_{1}\text{ cos }60^{^\circ }=\frac{3 V_{0}}{2}\text{ cos }30^{^\circ }\Rightarrow V_{1}=\frac{3 \sqrt{3}}{2}V_{0}$