Here, m 1 = m, m 2 = 2m

u 1 = 2 m/s, u 2 = 0

coefficient of restitution, e = 0.5

Let v 1 and v 2 be their respective velocities after collision.

Applying the law of conservation of linear momentum, we get

m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2

∴ m × 2 + 2m × 0 = m × v 1 + 2m × v 2

or 2m = mv 1 + 2mv 2

or 2 = (v 1 + 2v 2 ) ...(i)

By definition of coefficient of restitution,

e =

or e(u 1 – u 2 ) = v 2 – v 1

0.5(2 – 0) = v 2 – v 1 ...(ii)

1 = v 2 – v 1

Solving equations (i) and (ii), we get

v 1 = 0 m/s, v 2 = 1 m/s