In which of the following cases may forces not be required to keep the state of motion?

An open water-tight railway wagon of mass $5 \times 10^3 \text{ kg}$ coasts at an initial velocity $1.2 \text{ m/s}$ without friction on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after it has collected $10^3 \text{ kg}$ of water will be .............. $\text{m/s}$.

$A$ block of mass $10 \ kg$ moving with a velocity of $5 \hat{i} \ m \ s^{-1}$ on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass $4 \ kg$ moves with a velocity of $10 \hat{i} \ m \ s^{-1}$,then the velocity of the second piece is:

$A$ ball of mass $m$ is moving towards a wall with velocity $v$ at an angle $\theta$ with the normal to the wall, as shown in the diagram. In which direction is its linear momentum conserved?

$A$ 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?

$A$ 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