Question

A gun of mass M fires a bullet of mass with a kinetic energy E. The velocity of recoil of the gun is?

Answer 1

a gun of mass M fires a bullet of mass m with kinetic energy E. so, we have to find velocity of recoil of the gun.

we know, kinetic energy = 1/2 mv²

so, E = 1/2 mv²

or, v = √{2E/m} .......(1)

now applying law of conservation of linear momentum,

initial linear momentum = final linear momentum

or, m × 0 + M × 0 = mv + Mv'

[because both gun and bullet were in rest before firing so, velocity of bullet = velocity of gun = 0]

or, 0 = mv + Mv'

or, v' = -mv/M

from equation (1),

= -m√{2E/m}/M

= -√{2Em}/M [ here negative sign Indicates that recoil velocity of gun is just opposite of bullet's velocity ]

Answer 2

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