A simple pendulum has a string of length 2 m and a bob of mass m . The bob is released from rest when the string is horizontal. At the lowest point of its path, the bob strikes a stationary heavy block and loses 50 % of its kinetic energy in the collision. The maximum angle the string makes with the vertical during the subsequent rebound is:

Step-by-step solution

Let the length of the pendulum be L = 2 m . When released from the horizontal position, the initial height of the bob relative to the lowest point is h₁ = L . By conservation of mechanical energy, the kinetic energy of the bob just before impact at the lowest point is: K₁ = mgL During the collision, the bob loses 50 % of its kinetic energy. The kinetic energy remaining just after the collision is: K₂ = K₁ - 0.5K₁ = 0.5K₁ = 0.5mgL Let h₂ be the maximum height reached by the bob during the rebound. Equating the remai