$A$ bomb of $12 \ kg$ divides into two parts whose ratio of masses is $1 : 3$. If the kinetic energy of the smaller part is $216 \ J$,then the momentum of the bigger part in $kg \cdot m/s$ will be:

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then

Explain the conservation of linear momentum with a suitable example.

$A$ ball of mass $m$ strikes the inclined face of the wedge of mass $M$ normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before the collision. The conservation of momentum is applicable for the event of collision for:
$(i)$ $m$ as system,along $Y'$
$(ii)$ $M$ as system,along $Y'$
$(iii)$ $(M + m)$ as system,along $X$
$(iv)$ $(M + m)$ as system,along $Y$
Which of the following is correct?

$A$ 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 :

$A$ shell of mass $M$ initially at rest suddenly explodes into three fragments. Two of these fragments are of mass $M/4$ each, which move with velocities $3 \text{ m/s}$ and $4 \text{ m/s}$ respectively in mutually perpendicular directions. The magnitude of the velocity of the third fragment is: (in $\text{ m/s}$)