Two small balls A and B , each having mass m , are rigidly connected to the ends of a light rod of length L . The system translates on a frictionless horizontal surface with a velocity v₀ in a direction perpendicular to the rod. A particle P of mass m , initially at rest on the surface, sticks to the ball A upon collision. Calculate the velocity of the centre of mass C of the system A + B + P subsequent to the collis

Step-by-step solution

Let the initial direction of motion of the rod be along the positive x-axis. The system consists of three masses: ball A , ball B , and particle P . Mass of ball A , m_A = m Mass of ball B , m_B = m Mass of particle P , m_P = m Initial velocities of the components are: v _A = v₀ i v _B = v₀ i v _P = 0 The total initial linear momentum of the system A + B + P is: P _i = m_A v _A + m_B v _B + m_P v _P P _i = m(v₀ i ) + m(v₀ i ) + m(0) = 2mv₀ i Since there are no external horizontal forces acting on the system, the to