Question

A horizontal plane supports a stationary vertical cylinder of radius $R$ and a pebble attached to the cylinder by a horizontal thread AB of length $l_0$ as shown in top view of cylinder and pebble system. The pebble is given a velocity $v_0$. How long will it take to strike the cylinder. Assume no friction.

• A. $\frac{l_0}{v_0}$
• B. $\frac{l_0^2}{R{v}_0}$
• C. $\frac{l_0^2}{2R{v}_0}$
• D. $\frac{l_0^3}{3R^2{v}_0}$

Answer 1

Answer: (C)

$\frac{l_0^2}{2R{v}_0}$

Let s be the total distance covered by disc.
Then $t=\frac{s}{v_0}$.
At any instant $dx=(l_0-R\theta )d\theta$
$\therefore s={\int }_0^{l_0/R}(l_0-R\theta )d\theta =\frac{l_0^2}{R}-\frac{l_0^2}{2R}=\frac{l_0^2}{2R}$
$\therefore t=\frac{l_0^2}{2R{v}_0}$