A simple pendulum of length L has a bob of mass m . It is released from rest from a horizontal position. At the lowest point of its swing, the bob makes a head-on elastic collision with a stationary block of mass 3m resting on a smooth horizontal surface. The maximum height reached by the pendulum bob as it rebounds after the collision is

Step-by-step solution

Let the velocity of the pendulum bob just before the collision be u . By conservation of mechanical energy, as it falls from a horizontal position (height L ): u = 2gL The collision is head-on and elastic. The velocity v₁ of the bob of mass m after colliding with a stationary block of mass 3m is: v₁ = ( m - 3m m + 3m ) u v₁ = ( -2m 4m ) u = - u 2 The negative sign indicates that the bob rebounds. Its speed after the collision is u 2 . Let the maximum height reached by the bob during its rebound be h . Using conserv