From a rifle of mass $4 k g$ , a bullet of mass $50 g$ is fired with a velocity of $35 {m s}^{- 1}$ with respect to the ground. Calculate the recoil velocity of the rifle.

$1 {m s}^{- 1}$

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$0.4375 {m s}^{- 1}$

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$2.5 {m s}^{- 1}$

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$0 {m s}^{- 1}$

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Solution

The correct option is B
$0.4375 {m s}^{- 1}$

Let initial velocity of bullet be $u_{1}$ and initial velocity of rifle be $u_{2}$ .
$u_{1} = u_{2} = 0$ (Initially bullet and rifle system was at rest)
Let, mass of rifle , $m_{1}$ = $4 k g$

Mass of bullet, $m_{2}$ = $\frac{50}{1000} = 0.05 k g$

Final velocity of bullet, $v_{2}$ = $35 {m s}^{- 1}$
Final velocity of rifle, $v_{1}$ = v

From principle of conservation of linear momentum:
Initial momentum is equal to final momentum.
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
$4 \times 0 + 0.05 \times 0 = 4 \times v + 0.05 \times 35$
$0 = 1.75 + 4 v$
$\Rightarrow$ $v = - 0.4375 m s^{- 1}$

The negative sign indicates that the rifle recoils with the velocity of $0.4375 {m s}^{- 1}$ .

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