$A$ constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k} \text{ N}$ causes a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k} \text{ m}$ in $2 \text{ s}$. The work done and the power are respectively:

In a perfectly inelastic collision, two spheres made of the same material with masses $15 \ kg$ and $25 \ kg$, moving in opposite directions with speeds of $10 \ m/s$ and $30 \ m/s$, respectively, strike each other and stick together. The rise in temperature (in $^{\circ}C$), if all the heat produced during the collision is retained by these spheres, is: (specific heat of sphere material $31 \ cal/kg \cdot ^{\circ}C$ and $1 \ cal = 4.2 \ J$)

State if each of the following statements is true or false. Give reasons for your answer.
$(a)$ In an elastic collision of two bodies,the momentum and energy of each body is conserved.
$(b)$ Total energy of a system is always conserved,no matter what internal and external forces on the body are present.
$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.
$(d)$ In an inelastic collision,the final kinetic energy is always less than the initial kinetic energy of the system.

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass $1.00 \; g$ falling from a height $1.00 \; km$. It hits the ground with a speed of $50.0 \; m s^{-1}$. $(a)$ What is the work done by the gravitational force? $(b)$ What is the work done by the unknown resistive force?

$A$ small disc of mass $m = 1 \,g$ slides down a smooth hill of height $h = 10 \,cm$ from rest and gets onto a plank of mass $M = 100 \,g$ as shown in the figure. Due to friction between the disc and the plank, the disc slows down and moves as one piece with the plank. The work done by the frictional force is approximately (Use $g = 10 \,m/s^2$): (in $\,J$)

$A$ ball strikes against the floor and returns with double the velocity; in which type of collision is it possible?