$A$ spacecraft of mass $M$ is moving with velocity $V$ and suddenly explodes into two pieces. $A$ part of it of mass $m$ comes to rest. The velocity of the other part will be:

$A$ girl riding a bicycle along a straight road with a speed of $5 \, m/s$ throws a stone of mass $0.5 \, kg$ which has a speed of $15 \, m/s$ with respect to the ground along her direction of motion. The mass of the girl and bicycle is $50 \, kg$. Does the speed of the bicycle change after the stone is thrown? What is the change in speed,if so?

$A$ $100\, g$ iron ball having velocity $10\, m/s$ collides with a wall at an angle of $30^\circ$ with the wall and rebounds with the same angle. If the period of contact between the ball and the wall is $0.1\, s$,then the force experienced by the wall is ........... $N$.

$A$ spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released,the spring exerts equal and opposite average forces for the same time on each toy cart. If $v_1$ and $v_2$ are the velocities of the toy carts and there is no friction between the toy carts and the ground,then :

$A$ stationary particle explodes into two particles of masses $m_1$ and $m_2$ which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $E_1/E_2$ is:

$A$ particle of mass $m$ is moving along the $x$-axis with a speed $v_0$. Suddenly,a part of its mass,$m/3$,breaks off and moves parallel to the $y$-axis with a speed $2v_0$. Find the velocity of the remaining part in terms of unit vectors.