# A string with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass  of 2 kg attached to it at a distance of 1 m from the wall. A mass  of 0.5 kg is attached to the free end. The system is initially held at rest so that the string is horizontal between wall and pulley and vertical beyond the pulley as shown in Fig. The system is released from the rest from the position as shown The ratio of velocity of  and  when  strikes the wall is a) b) c) d)

## Question ID - 101227 | SaraNextGen Top Answer A string with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass  of 2 kg attached to it at a distance of 1 m from the wall. A mass  of 0.5 kg is attached to the free end. The system is initially held at rest so that the string is horizontal between wall and pulley and vertical beyond the pulley as shown in Fig. The system is released from the rest from the position as shown The ratio of velocity of  and  when  strikes the wall is a) b) c) d)

Answer Key / Explanation : (a) -

(a)

When  strikes the wall, vertically downward component of its displacement from initial position is 1 m and its distance from pulley  is

While its initial distance from the pulley was  It means vertically upward displacement of mass  is

Let  strike the wall with velocity  Since the string between the two blocks always remains taut, therefore at any instant speed of  is equal to that component of velocity of which is along the string . Hence, velocity of  when  strikes the wall is  where

According to law of conservation of energy, loss of potential energy of  increase in of of of