Question

Six bullets of mass $5\text{gm}$ are fired from a gun of mass $5\text{kg}$. What is the speed of the gun if the speed of the bullets w.r.t. the ground is $200\text{m/s}$?

• A. $0.2\text{m/s}$
• B. $200\text{m/s}$
• C. $1.2\text{m/s}$
• D. $\frac{200}{6}\text{m/s}$

Answer 1

The correct option is C $1.2\text{m/s}$

As there is no external force on the system, linear momentum of the system will be conserved.

From momentum conservation
$\sum p_i=\sum p_f$
$\sum (mv{)}_i=\sum (mv{)}_f$
$\Rightarrow 0=m_g{v}_g+6m_b{v}_b$
$\Rightarrow 5\times v_g=-6\times \frac{5}{1000}\times 200$
$\Rightarrow 5\times v_g=-6$
or $v_g=-1.2\text{m/s}$
(-ve sign means opposite to the dirction of bullets)