Two particles $A$ and $B$ of masses $2 \mathrm{kg}$ and $3 \mathrm{kg}$ moving on a smooth horizontal surface with speed $1.5 \mathrm{m} {\mathrm{s}}^{-1}$ and $2 \mathrm{m} {\mathrm{s}}^{-1}$collide perfectly inelastically, then

A particle strikes a smooth horizontal surface at an angle $\theta >0$ and it rebounds at an angle $\varphi$ as shown

Friction between the rigid rod of mass $m$ and wedge of mass $2m$ is zero while the coefficient of friction between ground and wedge is $0.1$. A force $F$ is applied on the wedge, so that rod moves with constant velocity ${\mathrm{v}}_0=5 \mathrm{m} {\mathrm{s}}^{-1}$ in upward direction as shown. What will be the power($\mathrm{W}$) delivered by force $F$ ? (take $m=1 \mathrm{kg}, \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)