Question

A bullet of mass 80 g is fired with velocity of 250 m/s from a rifle of mass 5 kg
Calculate the recoil velocity of the rifle. 4 ms.yooon's
OR​

Answer 1

$\large {\textsc {\bold {\underline {Given:}}}}$

• Mass of the bullet = 80 g
• Velocity of the bullet = 250 m/s
• Mass of the rifle = 5 kg

$\large {\textsc {\bold {\underline {To\ find:}}}}$

• Recoil velocity of the rifle.

$\large {\textsc {\bold {\underline {Solution:}}}}$

Mass of the rifle ($\sf m_{1}$) = 5 kg

Mass of the bullet ($\sf m_{2}$) = 80 g =  0.08 kg

We have to find, recoil velocity of the rifle. ($\sf v_{1}$)

The bullet is fired with an initial velocity ($\sf v_{2}$) of 250 m/s

Initially, the rifle is at rest.

Thus, its initial velocity (v) = 0

Total initial momentum of the rifle and bullet :-

⇒  ($\sf m_{1} + \sf m_{2}$) × v = 0

The total momentum of the rifle and bullet system after firing

= $\sf m_{1} \times \sf v_{1} + \sf m_{2} \times \sf v_{2}$

= (5 × $\sf v_{1}$) + (0.08 × 250)

= 5$\sf v_{1}$ + 20

According to the law of conservation of momentum :-

Total momentum after the firing = Total momentum before the firing

So,

5$\sf v_{1}$ + 20 = 0

$\sf v_{1}$ = $\sf\dfrac{-20}{5}$

$\sf v_{1}$ = -4 m/s

$\large {\textsc {\bold {\underline {Recoil\ Velocity:}}}}$

Recoil velocity of the rifle is -4 m/s.

Hope it helps!!

Answer 2

Given:-

• Mass of bullet = 80 g or 0.08 kg

• Mass of gun = 5 kg

• Velocity of bullet = 250 m/s

To Find:-

• Recoil velocity of rifle.

Solution:-

Here, We know that

Mass of bullet × Velocity of bullet = Mass of Gun × Recoil velocity of gun

⇒ 0.08 kg × 250 m/s = 5 kg × -v m/s  

⇒ 20 kg-m/s = -5v kg-m/s

⇒ v = -$\dfrac{20}{5}$ m/s  or  -4 m/s

∴ The Recoil Velocity of the rifle is -4 m/s

[Note:- It will negative because it is in opposite direction of firing ]

Some Important Terms:-

• Law of Conservation of Linear momentum:-

Total momentum before collision = Total momentum after collision

that is,      m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where, m₁ = mass of first object

            m₂ = mass of second object

            u₁  = initial velocity of first object

            u₂ = initial velocity of second object

            v₁  = final velocity of first object

            v₂ = final velocity of second object