A body of mass `m_1 = m` moving with a velocity `v_1 = v` in the x-direction collides with another body of the same mass `m_2 = m` moving in the y-direction with the same speed `v_2 = v`. Then coalesce into one body during the collision.
The magnitude of the momentum of the composite body is

Options

A. `mv `
B. `sqrt(2) mv`
C. `2mv `
D. `2sqrt(2) mv`

Answer

B

Explanation

Let v. be the velocity of the composite body and let `theta` be the angle which the velocity vector v. make with X-axis
conservation of x and y components of momentum gives
`m_1 v_1 = (m_1 + m_2)v. cos theta implies mv = 2mv. cos theta " " .....(1)`
`m_2 v_2 = (m_1 + m_2) v. sin theta implies mv = 2 mv. sin theta " " ....(2)`
Squaring and adding Eqs. (1) and (2), we get
`2(mv)^2 = (2mv.)^2 = 2mv. = sqrt(2)mv " " ..........(3)`
Momentum of the composite body is 2 mv..