A very heavy block of mass M moving horizontally with a speed of 2 ms ⁻¹ elastically collides with a small pendulum bob of mass m initially at rest, where M m . The bob is suspended by a light string. Taking g = 10 ms ⁻² , the maximum vertical height reached by the pendulum bob after the collision is:

Step-by-step solution

In a 1D elastic collision where a very heavy object ( M ) collides with a light stationary object ( m ), the light object acquires approximately twice the initial velocity of the heavy object. v_ bob = 2v = 2 2 = 4 ms ⁻¹ . By conservation of mechanical energy for the pendulum swing, the kinetic energy of the bob just after the collision is converted entirely into gravitational potential energy at its maximum height: 1 2 m v_ bob ^2 = mgh h = v_ bob ^2 2g = 4^2 2 10 = 16 20 = 0.8 m. Answer: 0.8 m