A point mass M moving with a certain velocity collides with a stationary point mass M / 2 . The collision is elastic and in one-dimension. Let the ratio of the final velocities of M and M / 2 be x . The value of x is

Step-by-step solution

As collision is elastic both linear momentum and kinetic energy are conserved. We have, following given condition, Momentum conservation gives, M u 1 = M v 1 + M 2 v 2 ⇒ 2 u 1 = 2 v 1 + v 2 . . . ( i ) Energy conservation gives, 1 2 M u 1 2 = 1 2 M v 1 2 + 1 2 M 2 v 2 2 ⇒ 2 u 1 2 = 2 v 1 2 + v 2 2 . . . ( ii ) Now, substituting for u 1 from Eq. ( i ) in Eq. ( ii ) , we get 2 2 v 1 + v 2 2 2 = 2 v 1 2 + v 2 2 ⇒ 4 u 1 2 + v 2 2 + 4 v 1 v 2 = 4 v 1 2 + 2 v 2 2 ⇒ v 2 2 = 4 v 1 v 2 or v 1 v 2 = 1 4 ∴ Ratio of final velo