Question

A 15 g bullet is fired from a gun of mass 2kg with a speed of 1000 m/s find recoil velocity of gun

Answer 1

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weight of bullet × initial speed of bullet / weight of gun = recoil velocity of gun

15 g

= 0.015 kg

0.015 kg × 1000 m/s /2 kg

= 7.5 m/s

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Answer 2

Acc. to law of conservation of momentum,

initial momentum of the system = final momentum of the system

initial momentum of bullet+initial momentum of gun = final momentum of bullet+ final momentum of gun

initial momentum of gun = mass of gun × initial velocity of gun

initial velocity of gun = 0 m/s (it is at rest)

mass of gun = 2kg

initial momentum of gun = 2×0= 0 kg m/s

initial momentum of bullet = initial velocity of bullet × mass of bullet

initial velocity of bullet = 0 m/s

mass = 0.015 kg

initial momentum of bullet = 0.015×0=0 kg m/s

final momentum of bullet= mass of bullet × final velocity of bullet

= 0.015 kg × 1000 m/s

= 15kg m/s

momentum of gun = mass of gun × velocity of gun

= 2 × velocity

initial momentum of system = final momentum of system

0+0 =15 + 2 velocity

-15 = 2 velocity

recoil velocity of gun = -7.5 m/s