In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ………… $\mathrm{ergs}$

In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at

Answer carefully, with reasons :

$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?

$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?

(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly ………….. $\mathrm{h}$

If the kinetic energy of a body is directly proportional to time $t$, the magnitude of force acting on the body is 
$(i)$ directly proportional to $\sqrt t$
$(ii)$ inversely proportional to $\sqrt t$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of body