A continuous stream of particle of mass m and velocity v, is emitted from the 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

Engineering

Physics

Collision

Variable Mass System

Momentum and Energy Conservation for System of Particles

Question

A continuous stream of particle of mass m and velocity v, is emitted from the 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

$\frac{Nm + M}{mv}$

$\frac{mv}{Nm + M}$

$\frac{mvN}{Nm + M}$

$\frac{mvn}{Nm + n}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

This involves conservation of momentum. The system's total initial momentum equals its total final momentum. Initially, the large mass M is at rest (momentum=0). The momentum from N particles, each with mass m and velocity v, is $N \times m v$ . Finally, the combined mass (M + Nm) moves with some velocity V.

Setting initial momentum equal to final momentum:

$0 + N m v = (M + N m) V$

Solving for V:

$V = \frac{N m v}{M + N m}$

Final Answer: $\frac{m v N}{N m + M}$