Question

A bullet of mass $0.1kg$ is fired with the speed of $100\frac{m}{s}$, the mass of the gun being $50kg$. The velocity of recoil is:

• A. $0.05\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• B. $0.5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• C. $0.2\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• D. $0.1\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Answer 1

The correct option is C

$0.2\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step-1: Given data

Mass of the bullet, $m=0.1kg$

Speed of the bullet, $u=100m/s$.

mass of gun, $M=50kg$.

Step-2: Finding the velocity of recoil

As there are no external force, on conserving momentum we get:

$$\begin{gathered} m\times u=M\times v \\ 0.1\times 100=50\times v \\ v=0.2\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \end{gathered}$$.

Hence recoil velocity is $0.2\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ and correct option is (c).