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.

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 in the opposite direction with the velocity of $0.4375 {m s}^{- 1}$ .

Suggest Corrections

Similar questions

Q. Question 3
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m

s^{- 1}

. Calculate the initial recoil velocity of the rifle.

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s⁻¹. Calculate the initial recoil velocity of the rifle.

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.

Join BYJU'S Learning Program

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with a velocity of 35 ms−1​ with respect to the ground. Calculate the recoil velocity of the rifle.

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.