A mass 'm' moves with a velocity 'v' and collides inelastieally with another identical mass . After collision the `1^(st)` mass moves with velocity `v/sqrt3` in a direction perpendicular to the initial direction of motion. Find the speed of the `2^(nd)` mass after collision.
`undersetunderset ((before),(collision))(m)(*rarr) underset(m)* uparrow v//sqrt3 underset((after),(collision):)`

Options

A. `(2v)/(sqrt(3))`
B. `(v)/(sqrt(3))`
C. `v`
D. `sqrt(3) v`

Answer

A

Explanation

In the collision , the momentum is conserved. Before the collision momentum is along the `x`-axis , after the collision , the resultant momentum should be along the `x`-axis , for this the second particle should move at some angle with the `x`-axis. Here , the momentum should be conserved in the `x`-axis and `y`-directions separately.
Momentum conservation :
`x`-axis : mv = mV cos theta rArr V cos theta = v`
`y`-ax is: 0 = m(v)/(sqrt(3)) - m V sin theta rArr V sin theta = (v)/(sqrt(3))`
`V = sqrt((V sin theta)^(2) + (V cos theta)^(2)) = ( 2v)/(sqrt(3))`