A bullet of mass $40 g$ is horizontally fired with a velocity $100 m s^{- 1}$ from a pistol of mass $2 k g$ . What is the recoil velocity of the pistol ?

2 ms^-1

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

20 ms^-1

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

-1 ms^-1

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

15 ms^-1

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

Open in App

Solution

The correct option is A
2 ms^-1

Given, mass of bullet $m_{b} = 40 g = \frac{40}{1000} = 0.04 k g$ , mass of pistol, $m_{p} = 2 k g$
Initial velocity of bullet, $u_{b}$ and pistol, $u_{p}$ is zero. (as initially both objects were at rest)
Final velocity of the bullet, $v_{b} = 100 m s^{- 1}$
Let recoil velocity of the pistol be $v_{p}$
From law of conservation of momentum, total initial momentum of the system before firing = total final momentum of the system after firing.
$∴$ $(m_{b} \times u_{b}) + (m_{p} \times u_{p}) = (m_{b} \times v_{b}) + (m_{p} \times v_{p})$
$\Rightarrow$ $0 = (0.04 \times 100) + (2 \times v_{p})$
$\Rightarrow$ $0 = 4 + (2 \times v_{p})$
$\Rightarrow v_{p} = \frac{- 4}{2} = - 2 m s^{- 1}$ (negative sign shows that the pistol recoils after firing)
$∴$ Recoil velocity of the pistol is $2 m s^{- 1}$

Suggest Corrections

Similar questions

What is the velocity of recoil of a gun, if a bullet of mass 100 g is fired from a gun of mass 20 kg with a velocity fo 100 ms^–1?

A bullet of mass 20g is horizontally fired with a horizontal velocity 150m/s from a pistol of mass 2kg. What is the recoil velocity of the pistol?