A particle at rest is constrained to move on a smooth horizontal surface. Another identical particle hits the fractional particle with a velocity `v` at an angle `theta=60^(@)` with horizontal. If the particles move together, the velocity of the combination just after 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 them. Since no net force is acting on the system of particle parallel to the surface, conservation of linear momentum along the direction yields the following result
`mvcostheta=(m+m)v'impliesv'=v/2cos60^(@)=v/4`