Question

A bullet of 5 g is fired from a pistol of 1.5 kg. If the recoil velocity of pistol is 1.5 m/s, find the velocity of bullet. (in m/s)

• A. 450 m/s
• B. 400 m/s
• C. 500 m/s
• D. 600 m/s

Answer 1

The correct option is A

450 m/s

Here we have,

Mass of bullet, m₁ = 5 g = $\frac{5}{1000}$ kg = 0.005 kg

Mass of pistol, m₂= 1.5 kg

Recoil velocity of pistol v₂ = 1.5 m/s

Velocity of bullet v₁= ?

Since, before firing, the bullet and pistol are in rest, thus

Initial velocity of bullet, u₁=0

And initial recoil velocity of pistol, u₂ =0

We know that,

m₁u₁+m₂u₂ = m₁v₁+m₂v₂

(0.005 kg x 0) + (1.5 kg x 0) = (0.005 kg x v₁) + (1.5 kg x 1.5 m/s)

0 = (0.005 kg x v₁) + (2.25 kgm/s)

0.005 kg x v₁ = -(2.25 kgm/s)

v₁ = $\frac{-2.25kgm/s)}{0.005kg}$ = -450 m/s

Thus, velocity of bullet = 450 m/s, here negative sign with velocity of pistol shows that, bullet moves in the opposite direction of recoiling of the gun.