Question

A particle A of mass $2m$ is held on a smooth horizontal table and is attached to one end of an inelastic string which runs over a smooth light pulley at the edge of the table. At the other end of the string there hangs another particle B of mass m, the distance from A to the pulley is l. The particle A is then projected towards the pulley with velocity u.
a. Find the time before the string becomes taut, the initial velocity of A and B is $4u/3$.

• A. $2\frac{3u}{g}$
• B. $2\frac{2u}{g}$
• C. $2\frac{4u}{g}$
• D. $2\frac{u}{g}$

Answer 1

The correct option is D $2\frac{u}{g}$

Let 'V' be the common velocity.

When A reaches pulley. $A$ & $B$ will move with common velocity $T$ if string is tavt. So, if A travel distance l, B should also travel ${}^{\prime }{l}^{\prime }$ in the same time.

Let time taken is 't'

$u\times t=\frac{1}{2}g{t}^2$

$t=\frac{2u}{g}$