A block of mass 4 m travelling at a velocity `v_1` in x-direction on a frictionless horizontal plane makes a head-on collision with another block of mass 2 m travelling in opposite direction with a velocity `v_2` . After collision, both the blocks travel as a single block along x-direction with a final velocity `5v_2` . The ratio of velocities i ` v_1/v_2` is

Options

A. 2
B. 3
C. 5
D. 8

Answer

D

Explanation

Momentum before collision
`P_1 = 4mv_1 = 2mv_2`
Momentum after collision
`P_2 = 6m (-5v_2) = - 30 mv^2 `
conservation of momentum gives
`P_1 = P_2`
`rArr 4mv_1 - 2mv_2 = - 30 mv_2 " " rArr 4v_1 = - 32 v_2`
` rArr v_1/v_2 = (-32)/(4) = - 8 " or " |v_1/v_2| = 8`