a gun of mass X fires a bullet of mass 25g with a velocity of 40 m/s . calculate the value of X , if the recoil velocity of gun iz 0.5 m/s plz help

Let m and X be the masses of the bullet and the gun respectively.

Since both are at rest, their speeds will be zero.

u₁ = 0  u₂ = 0

∴Total momentum of the bullet-gun system before firing,

= mu₁ + mu₂= 0

After firing

Let v and V be the velocities of the bullet and the gun respectively.

∴Total momentum after firing = mv + XV

Now, from the law of conservation of momentum,

Momentum before firing = Momentum after firing

0 = mv + XV

m = 25g = 0.25kg  v = 40 m/s  V=-0.5 m/s (because it is opposite to v)

X=2kg.