A bullet of mass m moving horizontally with speed v 0 hits a wooden block of mass M that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height h then how much of the initial kinetic energy of the bullet is lost in the collision?

Step-by-step solution

Given: Mass of bullet m , the velocity of bullet v 0 and mass of the wooden block M . Let the velocity of the bullet after the collision with the wooden block be v Applying the law of conservation of momentum, we obtain m v 0 = M + m v v = m v 0 M + m Now applying the law of conservation of mechanical energy, we obtain 1 2 m v 0 2 = m g h Putting the value of v in the above equation, we get 1 2 M + m m v 0 M + m 2 = M + m g h Maximum height of the block-bullet system h = 1 2 m v 0 2 M m + M