Two identical horizontal spring-mass systems, P and Q, each with a block of mass M , are oscillating with an amplitude A on a frictionless surface. In system P, a small mass m is gently dropped onto the block when it is exactly at its mean position and sticks to it. In system Q, the identical small mass m is gently dropped onto the block when it is exactly at its extreme position and sticks to it. Consider the follow

Step-by-step solution

For system P, the mass m is added at the mean position where the velocity of block M is maximum. This is an perfectly inelastic collision. By conservation of linear momentum, Mv = (M+m)v' , so the velocity decreases. Since potential energy is zero at the mean position, the new total mechanical energy is purely the new kinetic energy, which is less than the initial kinetic energy. Thus, the new amplitude A' is less than A . For system Q, the mass m is added at the extreme position where the velocity is zero. No kine