Question

A body A of mass m moving with a velocity u undergoes an inelastic collision with another body B of mass 2m at rest. After the collision the first ball moves with a velocity μ/√3 in a direction perpendicular to its initial direction of motion. The ratio of final kinetic energy of B to that of A after collision is

(1) 1 : 2

(2) 2 : 1

(3) 3 : 1

(4) 1 : 4

Answer 1

(2) 2 : 1

Take velocity u (initial) of A as +x direction.

Let v₁ = μ/√3 and v₂ be velocity of A and B after collision as shown in Fig.

Applying principle of momentum conservation; Along x–direction, we have

2m v_2x mu [v_x is the x component of v_B after collision]

v_x = u/2

∴ Velocity of B after collision is given by