Question

From a rifle of mass 4 kg a bullet of mass 50 g is fired with an initial velocity of 35 ms^-1, then the initial recoil velocity of the rifle is-

1.

0.535 ms-1

2.

0.487 ms-1

3.

0.438 ms-1

4. 0.635 ms-1

Answer 1

Correct Answer - Option 3 :

0.438 ms-1

Concept:

Conservation of momentum: “If the resultant force acting on a system of bodies is zero, then the momentum of the system remains constant”. 

Linear Momentum before collision (P1) = Linear Momentum after the collision (P2)

P1 = m1u1 + m2u2

P2 = m1v1 + m2v2

m1u1 + m2u2 = m1v1 + m2v2

Where

m₁ and m₂ are the mass of bodies

u₁ and u₂ are the initial velocity of body

v₁ and v₂ are the final velocity of body

Calculation:

Given that

mass of rifle m₁ = 4 kg

mass of bullet m₂ = 50 gm

velocity of rifle and bullet before fire = 0

velocity of rifle after fire = v1 m/s

velocity of bullet after fire v₂ = 35 m/s

using momentum conservation equation

m1u1 + m2u2 = m1v1 + m2v2

⇒ 0 =  4×(-v₁) + 0.05×35

v₁ is negative because velocity of rifle is opposite to bullet

Therefore

v₁ = 0.438 m/s

Hence, recoil velocity of rifle is 0.438 m/s.