$A$ man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun has a mass of $1 \,kg$. With what velocity does the gun recoil backwards?

Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

$A$ body of mass $M$ at rest explodes into three pieces,in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, m/s$ and $40 \, m/s$ respectively. The velocity of the third piece will be ............... $\, m/s$.

$10m$ is the total mass of a cannon that includes all shells. Initially, the cannon is moving with a velocity of $10 \ m/s$ along a horizontal frictionless path. If the cannon fires $n$ shells of mass $m$ in the direction of motion of the cannon one by one with velocity $u$ with respect to the ground, which of the following statements is correct? (Neglect any friction force)

$A$ bomb of mass $12\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3$. The $K.E.$ of the smaller fragment is $216\,J$. The momentum of the heavier fragment is (in $kg\cdot m/s$):

At a certain height,a body at rest explodes into two equal fragments with one fragment receiving a horizontal velocity of $10\sqrt{3} \text{ m/s}$. The horizontal distance between the two fragments,when their displacement vectors are inclined at $60^{\circ}$ relative to each other,is (take $g = 10 \text{ m/s}^2$):