Question

find the recoil velocity of a gun having mass equal to 5kg, if a bullet of 25gm acquires the velocity of 500m/s after firing from the gun​

Answer 1

Here given,

Mass of bullet (m1) = 25 gm = 0.025 kg

Velocity of bullet before firing (u1) = 0

Velocity of bullet after firing (v1) = 500 m/s

Mass of gun (m2) = 5 kg

Velocity of gun before firing, (u2) = 0

Velocity of gun after firing = ?

$m_{1}u_{1} +m_{2}u_{2}= m_{1}v_{1} +m_{2}v_{2}\\0.025 kg X 0 +5kg X 0=0.025 kg X 500m/s +5kgX v_{2}\\0= 12.5 kgm/s +5kgv_{2}\\-12.5 kgm/s = 5kgv_{2}\\v_{2} = -2.5kg m/s$

Thus, recoil velocity of gun is equal to 2.5 m/s. Here negative (- ve) sign shows that gun moves in the opposite direction of bullet