A sphere and a cube of equal masses on a horizontal frictionless floor, are confined between two vertical walls, as shown in the figure. The cube is attached to the wall by a massless spring. At the equilibrium position of the spring, the sphere just touches the cube. The cube is moved towards the left by a small amount from its equilibrium position, compressing the spring and is released at t = 0 . The system keeps

Step-by-step solution

Let the mass of the cube and the sphere be m . Let the spring constant be k . When the cube is released from a compression , it undergoes simple harmonic motion. It reaches the equilibrium position in time t₁ = 1 4 2 m k = 2 m k . At this position, the velocity of the cube is maximum, given by v = = k m . Since the sphere is at rest at the equilibrium position and has the same mass m , an elastic collision results in an exchange of velocities. The cube comes to rest, and the sphere acquires the velocity v . The sph