Question

A bullet of mass of $0.01kg$ is fired from a gun weighing $5.0kg$. If the initial speed of the bullet is $250m{s}^{-1}$, calculate the speed with which the gun recoils.

• A. $-0.5m/s$
• B. $-0.25m/s$
• C. $+0.5m/s$
• D. $+0.25m/s$

Answer 1

The correct option is A

$-0.5m/s$

Explanation of correct option

(A): $-0.5m/s$

Step 1: Given data

Mass of bullet= $0.01kg$

Mass of gun= $5.0kg$

Velocity of bullet= $250m{s}^{-1}$

Step 2: Finding the velocity of the gun

As per the law of Conservation of momentum,

$$\begin{gathered} 0={\mathrm{M}}_{\mathrm{bullet}}.{\mathrm{V}}_{\mathrm{bullet}}+{\mathrm{M}}_{\mathrm{gun}}.{\mathrm{V}}_{\mathrm{gun}} \\ {\mathrm{M}}_{\mathrm{bullet}}.{\mathrm{V}}_{\mathrm{bullet}}=-{\mathrm{M}}_{\mathrm{gun}}.{\mathrm{V}}_{\mathrm{gun}} \end{gathered}$$

${\mathrm{V}}_{\mathrm{gun}}=\frac{-{\mathrm{M}}_{\mathrm{bullet}}.{\mathrm{V}}_{\mathrm{bullet}}}{{\mathrm{M}}_{\mathrm{gun}}}$

$$\begin{gathered} {\mathrm{V}}_{\mathrm{gun}}=-{\mathrm{M}}_{\mathrm{bullet}}.\frac{{\mathrm{V}}_{\mathrm{bullet}}}{{\mathrm{M}}_{\mathrm{gun}}} \\ \mathrm{Putting}\mathrm{all}\mathrm{the}\mathrm{values}, \end{gathered}$$

${\mathrm{V}}_{\mathrm{gun}}=\frac{-0.01\mathrm{kg}\mathrm{x}250{\mathrm{ms}}^{-1}}{5.0\mathrm{kg}}$

${\mathrm{V}}_{\mathrm{gun}}=-0.5{\mathrm{ms}}^{-1}$

Hence, when a bullet of mass of $0.01kg$ is fired from a gun weighing $5.0kg$. If the initial speed of the bullet is $250m{s}^{-1}$ then the gun recoils at $-0.5m{s}^{-1}$. Hence option (a) is correct.