Question

8. A bullet of mass 10 gm is fired with an initial velocity of 20 m/s from a rifle of mass 4 kg. Calculate the initial recoil velocity of the rifle? a) v = +0.05m/s b) v = -0.05m/s c) v = -0.5m/s d) v = +0.5m/s

Answer 1

$b)=-0.05ms^-1$

Answer 2

Given :

• mass of bullet, m₁ = 10 g = 0.01 kg
• bullet is fired with a velocity , v₁ = 20 m/s
• initially bullet will be at rest, therefore initial velocity of bullet will be, u₁ = 0

• mass of rifle, m₂ = 4 kg
• initially rifle will be also at rest, therefore initial velocity of rifle will be, u₂ = 0

To find :

• recoil velocity of Rifle, i.e, final velocity of Rifle , v₂ = ?

Knowledge required :

• Formula to calculate momentum

      momentum = mass × velocity

• Law of conservation of momentum

    → initial momentum of system = final momentum of system

     →    m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

[ where m₁ and m₂ are masses of two objects , u₁ and u₂ are initial velocity of two objects, v₁ and v₂ are final velocities of two objects ]

The total momentum of a closed system is constant.

During a collision the total initial momentum of the system is equal to the total final momentum.

     

Solution :

Using law of conservation of momentum

→  m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

→ (0.01) (0) + (4) (0) = (0.01) (20) + (4) v₂

→ 0 = 0.2 + 4 v₂

→ v₂ = -0.2 / 4

→ v₂ = -0.05 m/s

     

therefore,

• Recoil velocity of Rifle is -0.05 m/s

( negative velocity shows that Gun will recoil in opposite direction ).

Hence,

OPTION (B) v = - 0.05 m/s is correct.