Question

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.

• A. $\frac{3\sqrt{3}}{2}{v}_0$
• B. $\frac{3}{2}{v}_0$
• C. $v_0$
• D. perpendicular to velocity of point $Q$ ( $Q$ and $C$ are at same horizontal level)

Answer 1

Answer: (A)

$V_1\text{ cos }60^{{}^{\circ }}=\frac{3V_0}{2}\text{ cos }30^{{}^{\circ }}\Rightarrow V_1=\frac{3\sqrt{3}}{2}{V}_0$