Question

A bullet of mass 30 g is fired from a gun with initial
velocity of 40 m/s. If mass of the gun is 5 kg, then
the recoil velocity of the gun is
(1) 22 m/s
(2) 24 m/s
(3) 2.2 m/s
(4) 0.24 m/s​

Answer 1

Answer:

0.24 m/s (Option 4)

Explanation:

As per the provided information in the given question, we have :

• Mass of bullet = 30 g ⇒ 0.03 kg
• Velocity of the bullet = 40 m/s
• Mass of the gun = 5 kg

We are asked to calculate the recoil velocity of the gun.

Let us suppose the recoil velocity of the gun as v.

According to the law of conservation of momentum , we can say that :

$\longmapsto \bf{Momentum_{(Bullet)} = Momentum_{(Gun)} }$

Calculating momentum of bullet :

$\longmapsto \rm {Momentum_{(Bullet)} = Mass_{(Bullet)} \times Velocity_{(Bullet)} }$

$\longmapsto \rm {Momentum_{(Bullet)} = (0.03 \times 40)\; kg.ms^{-1} }$

$\longmapsto \rm {Momentum_{(Bullet)} = \Bigg( \dfrac{3}{100} \times 40 \Bigg )\; kg.ms^{-1} }$

$\longmapsto \rm {Momentum_{(Bullet)} = \Bigg( \dfrac{3}{10} \times 4\Bigg )\; kg.ms^{-1} }$

$\longmapsto \rm {Momentum_{(Bullet)} = \Bigg( \dfrac{12}{10} \Bigg )\; kg.ms^{-1} }$

$\longmapsto \bf {Momentum_{(Bullet)} = 1.2 \; kg.ms^{-1} \dots (1)}$

Calculating momentum of gun :

$\longmapsto \rm {Momentum_{(Gun)} = Mass_{(Gun)} \times Recoil \; velocity_{(Gun)} }$

$\longmapsto \rm {Momentum_{(Gun)} = 5 \times v }$

$\longmapsto \rm {Momentum_{(Gun)} = 5v \; kg.ms^{-1} \dots (2) }$

Now, substitute the values from (1) and (2) in the equation of law of conservation of momentum.

$\longmapsto \bf{Momentum_{(Bullet)} = Momentum_{(Gun)} }$

$\longmapsto \rm{1.2 = 5v}$

$\longmapsto \rm{\dfrac{1.2 }{5} \; ms^{-1}= v}$

$\longmapsto \bf{0.24 \; ms^{-1} = 5v}$

∴ Recoil velocity of the gun is 0.24 m/s.