A body of mass 2 kg is moving with velocity 10 m / s towards east. Another body of same mass and same velocity moving towards north collides with former and coalsces and moves towards northeast. Its velocity is

Options

A. 10 m/s
B. 5 m/s
C. 2.5 m/s
D. `5sqrt(2)` m/s

Answer

D

Explanation

Initial momentum `= vec(P)= mv hat(i) + mv hat(j)`
`|vec(P)| = sqrt2mv`
Final momentum `=2m xx V`
By the law of conservation of momentum
`2m xx V= sqrt2mv rArr V= (v)/(sqrt2)`
In the problem `v= 10 m//s` (given) `therefore V= (10)/(sqrt2) = 5 sqrt2m//s`