A particle at rest is constrained to move on a smooth horizontal surface. Another identical particle hits the stationary particle with a velocity `v` at an angle `theta=60^(@)` with horizontal. If the particles move together, the velocity of the combination just after the impact is equal to

Options

A. `v`
B. `v//2`
C. `sqrt(3)v//4`
D. `v//4`

Answer

D

Explanation

The impact takes place along the line joining them. since the particle at rest is constrained to move on the horizontal surface. We cannot conserve the momentum along the line joining the. Since no net force is acting of the system of particles parallel to the surface, conservation of liner momentum along that direction yields
`mvcostheta=(m+m)v'impliesv'=v/2cos60^(@)=v/4`