Question

A bullet of mass 10 grams is fired from a gun of mass 6 kg with a velocity of 300 metres per second the recoil velocity of the gun is​

Answer 1

Given :

• Mass of Bullet = 10 grams

• Mass of Gun = 6 kg

• Velocity = 300 m/s

To Find :

• Recoil Velocity of the Gun

Solution :

Mass of Bullet = 10 gram

→ 10/1000 kg

→ 0.01 kg

Let's put the values in relation :

Mass of Bullet × Velocity of Bullet = Mass of gun × Recoil Velocity of gun

→ 0.01 × 300 = 6 × Recoil Velocity

→ 3 = 6 × Recoil Velocity

→ Recoil Velocity = 6/3

→ Recoil Velocity = 0.5 m/s

Recoil Velocity is always in negative as the direction of recoil is opposite to the direction of bullet.

Hence,Recoil Velocity is - 0.5 m/second

Answer 2

Given,

Mass of bullet = 10g

Mass of gun = 6kg

Both the bullet and gun are at rest before firing.

Momentum is mass times velocity

So,

Momentum of bullet before firing = 0

Momentum of gun before firing = 0

Therefore,

Momentum of the gun bullet system initially is zero.

The bullet is fired from the gun with a velocity = 300m/s

Momentum of bullet after firing = 10 * 10^-3 * 300 = 3 kgm/s

According to Law of conservation of linear momentum, The gun must recoil. Consider the recoil velocity to be x m/s

Momentum of gun after firing = 6x kgm/s

Since, No external force acts on the gun bullet system, The total linear momentum is conserved.

Momentum of the system before firing = Momentum of system after firing.

⇒0 = 3 + 6x

⇒ - 3 = 6x

⇒ x = - 0.5 m/s

Therefore, The gun recoils with 0.5 m/s in opposite to the direction in which bullet is fired.