Two pendulums each of length l are initially situated as shown in the figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision?

let m1, m2 be the mass of pendulums v1 be velocity of m1 before collision and v be the velocity of both the pendulums after collisionApplying the law of conservation of momentum,  m1v1=(m1+m2)V Where v1=2gd   is the velocity with which m1  collides with m2. Therefore, v =  m1(m1+m2)2gdNow, let the centre of mass rise through a height h after collision. In this case , the kinetic energy of (m1+m2) system is converted into potential energy at maximum height h ⇒12(m1+m2)V2=(m1+m2)gh⇒12(m1+m2){m1m1+m2}22gd=(m1+m2)gh⇒h=d{m1(m1+m2)}2