$A$ 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?

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man starts moving,then the velocity of the trolley $v_2$ with respect to ground will be

$A$ $1 \; kg$ stationary bomb explodes into three parts having mass ratio $1:1:3$. The parts with equal mass move in perpendicular directions with a velocity of $30 \; m/s$. What is the velocity of the third (heavier) part?

Three masses $m$,$2m$,and $3m$ are moving in the $x-y$ plane with speeds $3u$,$2u$,and $u$ respectively,as shown in the figure. The three masses collide at the same point $P$ and stick together. The velocity of the resulting mass 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

$A$ 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?