Question

A bullet of 50 g is fired using rifle of mass 10 kg. Rifle
recoils with velocity 2.5 m/s. Which of following is the
intial velocity of the bullet?

Answer 1

Given: mass of a bullet = 50 g = 0.05 g

           mass of the rifle = 10 kg

           velocity recoiled = 2.5 m/s

To Find: The initial velocity the bullet got on firing

Solution:

According to the law of momentum ,

$m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}$

where,

Mass of the bullet $m_{1}$ = 0.05 g

The velocity of the bullet before firing $u_{1}$= 0

Mass of the gun $m_{2}$ = 10 kg

The velocity of the rifle before firing $v_{1}$ = 0

The recoiled velocity of the rifle $v_{2}$ = 2.5 m/s

Let,

the velocity of the bullet after firing (Initial velocity) be = $v_{1}$

Hence, $m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}$

or. (0.05 × 0) + (10 × 0) = (0.05 × $v_{1}$) + (10 × 2.5)

or, $\frac{5}{100}$  $v_{1}$ + 25 = 0

or,  $v_{1}$ = -25 ×$\frac{100}{5}$

or  $v_{1}$ = - 500 m/s

Therefore, The velocity of the bullet is 500m/s

Concept:

Linear momentum -

• Linear Momentum is the product of a moving body's mass and velocity. P = mv [ where, P = Linear momentum, m= mass of the body, v = velocity produced]
• The total linear momentum is conserved when there is no external force applied on a system of several interacting particles.