$(a)$ State Newton's second law of motion. Use this law to find a method to measure force acting on an object.
$(b)$ From a rifle of mass $4 \ kg$,a bullet of mass $50 \ g$ is fired horizontally with an initial velocity of $40 \ m \ s^{-1}$. Calculate the initial recoil velocity of the rifle.

(D) Newton's second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
Mathematically,if $F$ is the force,$m$ is mass,$v$ is final velocity,$u$ is initial velocity,and $t$ is time:
$F \propto \frac{m(v-u)}{t}$
Since $\frac{v-u}{t} = a$ (acceleration),we get $F = kma$. By taking the constant $k = 1$,we derive the formula to measure force: $F = ma$.
$(b)$ Given:
Mass of rifle $(M)$ = $4 \ kg$
Mass of bullet $(m)$ = $50 \ g = 0.05 \ kg$
Velocity of bullet $(v)$ = $40 \ m \ s^{-1}$
Initial velocity of system = $0$
According to the law of conservation of momentum:
$MV + mv = 0$
$4 \times V + 0.05 \times 40 = 0$
$4V + 2 = 0$
$4V = -2$
$V = -0.5 \ m \ s^{-1}$
The negative sign indicates that the rifle recoils in the direction opposite to the bullet.