A particle of mass `m` moving eastward with a velocity `V` collides with another particle of same mass moving northwards with the same speed `V`. The two particles coalesce and the new particle moves in NE direction. Calculate magnitude and direction of velocity of new particle.

Options

A. `v//2`
B. 2v
C. `v//sqrt(2)`
D. v

Answer

C

Explanation

Initial momentum of the system
`vec(P)_(i)= mv hat(i) + mv hat(j)`
`|vec(P)_(i)|= sqrt2mv`
Final momentum of the system = 2mV
By the law of conservation of momentum
`sqrt2mv= 2mV rArr V= (v)/(sqrt2)`