Question

A bullet of mass 50gram is fired from a gun mass 6kg with the velocity of 400m/s.calculate the recoil velocity of the gun​

Answer 1

Answer:

Explanation:

Solution,

Here, we have

We know that

Mass of the bullet = 50 g

Mass of the gun = 6 kg

Velocity of the bullet = 400 m/s

To Find,

Recoil velocity of gun = ??

Let v be the recoil velocity of the gun.

Here, we know that,

In the absence of any external force, Momentum is conserved.

Momentum before firing = 0 (As gun and bullet inside the gun was in rest)

Momentum after firing = 50 × 10⁻³ × 400 × (-6) × v

Now, Here

By Law of conservation of mass,

We have,

⇒ 50 × 10⁻³ × 400 - 6 × v = 0

⇒ 50 × 10⁻³ × 400 × 6v = 0

⇒ 5 × 4 × 10³ × 10⁻³ = 6v

⇒ 20 = 6v

⇒ 20/6 = v

⇒ 10/3 = v

⇒ v = 3.33 m/s

Hence, the recoil velo0city of gun is 3.33 m/s.

Answer 2

Simply apply conservation of momentum.

Momentum before firing = 0 [ As gun and recoil both are at rest ]

Momentum after firing

= ( mass of bullet * velocity of bullet ) + ( mass of gun * - velocity of recoil )

[ -ve direction shows it falls backwards ]

= (0.05 * 400)+(6*(-v))

= (20)-6v

Now conservation momentum ,

20 - 6v = 0

⇒ 20 = 6v

⇒ v = 3.33 m/s

Hence the recoil velocity is 3.33 m/s