$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

$A$ 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

$10m$ 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)

$A$ shell of mass $5 M$, acted upon by no external force and initially at rest, bursts into three fragments of masses $M, 2 M$, and $2 M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2 v$ and $v$ respectively. The third fragment will

$A$ 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 :

$A$ projectile moving vertically upwards with a velocity of $200\, ms^{-1}$ breaks into two equal parts at a height of $490\, m$. One part starts moving vertically upwards with a velocity of $400\, ms^{-1}$. How much time will it take,after the break up,for the other part to hit the ground? .............. $s$