A continuous stream of particles, of mass `m` and velocity `r`, is emitted from a source at a rate of `n` per second. The particles travel along a straight line, collide with a body of mass `M` and get embedded in the body. If the mass `M` was originally at rest, its velocity when it has received `N` particles will be

Options

A. `(m vN)/(Nm + n)`
B. `(m vN)/(Nm + M)`
C. `(mv)/(Nm + M)`
D. `(Nm + M)/(mv)`

Answer

B

Explanation

Momentum of all particle colliding = final momentum
`implies Nm v = (M + m N) v_1`
`v_1 = (m vN)/(M + mN)`