Question

A bullet of mass $0.01\text{kg}$ is fired from a gun weighing $2\text{kg}$. Calculate the velocity with which the gun recoils if $10$ bullets are fired at the same time with a speed of $250\text{m/s}$. Consider $+vex$ axis along the direction of firing.

• A. $-12.5\text{m/s}$
• B. $-1.25\text{m/s}$
• C. $12.5\text{m/s}$
• D. $1.25\text{m/s}$

Answer 1

The correct option is A $-12.5\text{m/s}$

In the absence of external force on the system of (gun+bullet) along the $x$ direction, conservation of momentum will hold.
$\Rightarrow P_i=P_f..\left(i\right)$

Mass of gun, $m_{\text{gun}}=2\text{kg}$
Mass of bullet, $m_{\text{bullet}}=0.01\text{kg}$
Velocity of bullet $v_{\text{bullet}}=250\text{m/s}$
Momentum of $n$ bullets fired from the gun:
$=n\times m_{\text{bullet}}\times v_{\text{bullet}}$
$=10\times 0.01\times 250$
$=25\text{Ns}$

Let the recoil velocity of gun be $v$
Final momentum of system will be:
$P_f=25+m_{\text{gun}}v$
From Eq. $\left(i\right)$,
$P_i=P_f$
$\Rightarrow 0=25+m_{\text{gun}}v$
$\therefore v=-\frac{25}{2}=-12.5\text{m/s}$
Here $-ve$ sign represents that the gun will recoil along the $-vex$ axis.