A ball of mass m moving with a horizontal velocity v strikes the bob of a pendulum at rest. Mass of the bob of the pendulum is also m. During this collision, the ball sticks with the bob of the pendulum. The height to which the combined mass rises will be (g = acceleration due to gravity)

From the law of conservation of momentum,                      mv + m × 0 = (m + m)v'⇒                                    v'=mv(m+m)⇒v'=v2and we know that, h=u22g                                           (∵ v2-u2=2gh)Here,                     u=v'So,                        h=(v')22g                                                (∵ v'=v2)⇒                         h=v28g