Question

A bullet of mass 10 gm is fired with a velocity of 40 m/s from a gun of mass 8 kg. Find the recoil velocity (in m/s) of the gun.

Answer 1

Answer:

$\large{\underline{\boxed{\sf Velocity = 0.05 \: m/s}}}$

Explanation:

Actually, welcome to the concept of conservation of momentum. According to this, initial momentum should be equal to final momentum. Here,

$\rm P_{bullet} = P_{gun}$

For bullet -

Mass (m₁) = 10/1000 = 0.01 kg

Velocity (u₁) = 40 m/s =

For gun -

Mass (m₂) = 8 kg

Let the velocity be V.

According to the conservation of momentum ;

m₁ * u₁ = m₂ * V

⇒ 0.01 * 40 = 8 * V

⇒ 0.4 = 8V

⇒ V = $\sf \dfrac{0.4}{8}$

⇒ V = 0.05 m/s

Hence, the recoil velocity of the gun is 0.05 m/s.

Answer 2

Answer:

Explanation:

Given :-

Mass of the bullet, m₁ = 10 gm =  10/1000 = 0.01 kg

Initial velocity of the bullet, u₁ = 40 m/s

Mass of the gun, m₂ = 8 kg

To Find :-

Recoil velocity of the gun in m/s

Formula to be used :-

Conservation of momentum i.e v = (m₁ u₁)/m₂

Solution :-

Putting all the values, we get

⇒ v = (m₁ u₁)/m₂

⇒ v = 0.01 × 40/5

⇒ v = 0.01 × 5

⇒ v = 0.05 m/s

Hence, the recoil velocity of the gun is 0.05 m/s.