Question

A machine gun of mass$10kg$, fires the bullets of $10g$ at the rate of two every second. Each bullet comes up with a velocity of $2000m{{s}^{-1}}$. What will be the velocity of recoil of the gun at the end of the fourth second after firing starts?
$\begin{aligned} & A.1.6m{{s}^{-1}} \\\ & B.0.8m{{s}^{-1}} \\\ & C.3.2m{{s}^{-1}} \\\ & D.2.0m{{s}^{-1}} \\\ \end{aligned}$

Answer 1

The momentum of the bullet can be found by taking the product of the mass of the bullet and the velocity of the bullet. The mass of the bullet can be converted into kilograms by dividing this with thousands. According to the conservation of the momentum, the momentum of the bullet will be equivalent to the momentum of the gun. This will help you in answering this question.

Complete answer:
It has been mentioned in the question that the mass of the bullets coming out of the machine gun as,
$m=10g$
This can be converted into kilograms by dividing this with thousands. That is we can write that,
$m=10g=\dfrac{10}{1000}=0.01kg$
Velocity of the bullet can be written as,
$v=2000m{{s}^{-1}}$
The momentum of the bullet can be found by taking the product of the mass of the bullet and the velocity of the bullet. That is we can write that,
$P=mv=0.01\times 2000=20kgm{{s}^{-1}}$
According to the conservation of the momentum, this can be written as,
Momentum of the bullet will be equivalent to the momentum of the gun.
${{P}_{bullet}}={{P}_{gun}}$
This can be written as,
$20kgm{{s}^{-1}}=10\times v$
Rearranging the equation can be written as,
$v=\dfrac{20}{10}=2m{{s}^{-1}}$
Therefore the recoil velocity of the gun has been obtained as $2m{{s}^{-1}}$.

This has been mentioned as option D.

Note:
Momentum of the body can be defined as the quantity of the motion that a body has. A sports team which is moving can be considered for the system having momentum. The unit of the momentum can be expressed in kilogram metre per second. The momentum can be found to be a vector quantity.