$(a)$ Define momentum. Write its $SI$ unit.
$(b)$ $A$ bullet of mass $0.02 \ kg$ is fired from a gun weighing $7.5 \ kg$. If the initial velocity of the bullet is $200 \ m \ s^{-1}$,calculate the speed with which the gun recoils.

(N/A) Momentum is defined as the total quantity of motion possessed by a body. It is equal to the product of the mass and velocity of the body. Its $SI$ unit is $kg \ m \ s^{-1}$.
$(b)$ Given:
Mass of bullet $(m) = 0.02 \ kg$
Mass of gun $(M) = 7.5 \ kg$
Velocity of bullet $(v) = 200 \ m \ s^{-1}$
Recoil velocity of gun $(V) = ?$
According to the law of conservation of momentum,the total momentum before firing is equal to the total momentum after firing:
$m \times v + M \times V = 0$
$0.02 \times 200 + 7.5 \times V = 0$
$4 + 7.5 \times V = 0$
$7.5 \times V = -4$
$V = -4 / 7.5 = -0.533 \ m \ s^{-1}$
The negative sign indicates that the gun recoils in the direction opposite to the bullet. The speed of recoil is $0.533 \ m \ s^{-1}$.