A body of mass M moving at speed V 0 collides elastically with a mass m at rest. After the collision, the two masses move at angles θ 1 and θ 2 with respect to the initial direction of motion of the body of mass M . . The largest possible value of the ratio M m , for which the angles θ 1 and θ 2 will be equal, is :

Step-by-step solution

Linear momentum conservation (i) y -direction m v 2 sin θ = m v 1 sin θ m v 2 = m v 1 ...(1) (ii) x -direction m v 0 = m v 2 cos θ + m v 1 cos θ ...(2) from (1) and (2) m v 0 = m v 2 cos θ + m v 2 cos θ m v 0 = 2 m v 2 cos θ ...(3) (iii) e = 1 given v 2 - v 1 cos 2 θ v 0 cos θ = 1 v 2 - v 1 cos 2 θ = v 0 cos θ ...(4) v 2 - m 2 2 M cos 2 θ = v 0 cos θ v 2 1 - m M cos 2 θ = v 0 cos θ m v 0 2 m cos θ 1 - m M cos 2 θ = v 0 cos θ M