$A$ spacecraft of mass $M$ moves with velocity $V$ in free space at first,then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest,the other piece of spacecraft will have a velocity

$A$ body moving with speed $v$ in space explodes into two pieces of masses in the ratio $1 : 3$. If the smaller piece comes to rest,the speed of the other piece is

For a system to follow the law of conservation of linear momentum during a collision,the condition is:
$(1)$ Total external force acting on the system is zero.
$(2)$ Total external force acting on the system is finite and the time of collision is negligible.
$(3)$ Total internal force acting on the system is zero.

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

$A$ man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the platform,then the recoil velocity of the platform is:

$A$ system of $N$ particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?