Two balls having masses m and 2m are fastened to two light strings of same length l (figure 9-E 18). The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocities of the balls just after their collision. (b) How high will the balls rise after the collision?

Given that two balls having masses m and 2m are fastened to two light strings of same length l,

Let the velocity of m reaching at lower end is V₁,

From work energy principle

Similarly, velocity of heavy block will be

Therefore,

Since, both the balls acts in opposite direction.

{a} Let the final velocity of m and 2m is v₁ and v₂ respectively.

According to law of conservation of momentum

_________ (1)

Again,

_____________ (2)

Subtracting equation (2) from (1)

Putting in equation (2)

Hence, light ball will have velocity towards left

And heavy ball will velocity

{b} Let h be the height gone by heavy ball

Putting work energy principle

Similarly, h’ be the height reached by light ball

So, the balls will rise of following height after the collision

Light ball and heavy ball.