A bullet of mass 10 g is horizontally fired with a velocity 150  from a pistol of mass 5 kg. The recoil velocity of the pistol will be

CONCEPT:

• Momentum (P): The product of mass and velocity is called a momentum of the system.

Momentum (P) = Mass (m) × Velocity (V)

• Conservation of momentum: Whenever there is no net external force on the system then the total momentum of the system remains constant.

Initial momentum (P1) = Final momentum (P2)

CALCULATION:

• As there is no external force on the pistol and bullet system. So the total momentum of the system will remain constant.

Initially the system was in rest so velocity (V) = 0

Initial momentum (P1) = mass (m) × Velocity (V) = m × 0 = 0

After firing,

Velocity of bullet (Vb) = 150 m/s

Mass of bullet (mb) = 10 g = 10/1000 = 0.01 kg

Momentum of bullet (Pb) = mb × Vb = 0.01 × 150 = 1.5 kg m/s

Let recoil velocity of pistol = V m/s

Mass of rifle (mr) = 5 kg

Momentum of rifle (Pr) = mr × V = 5 × V = 5V kg m/s

Total final momentum of the system (P2) = Momentum of rifle + momentum of bullet = (5V + 1.5) kg m/s

According to conservation of momentum;

Initial momentum (P1) = Final momentum (P2)

0 = 5V + 1.5

V = - 1.5/5 = - 0.3  m/s

The negative sign denotes opposite direction. So the recoil velocity of pistol is 0.3 m/s.

Hence option 3 is correct.