$A$ rubber ball is dropped from a height of $5 \ m$ on a planet,where the acceleration due to gravity is not known. On bouncing,it rises to $1.8 \ m$. The ball loses its velocity on bouncing by a factor of

An object of mass $m$ is sliding down a hill of arbitrary shape and after traveling a certain horizontal path stops because of friction. The friction coefficient is different for different segments of the entire path but it is independent of the velocity and direction of motion. The work done that a force must perform to return the object to its initial position along the same path would be:

$A$ ball is falling freely from a height. When it reaches $10 ~m$ height from the ground, its velocity is $v_0$. It collides with the ground, loses $50 \%$ of its energy, and rises back to a height of $10 ~m$. Then the velocity $v_0$ is (in $~m / s$)

Water falls from a $40\,m$ high dam at the rate of $9 \times 10^{4}\,kg$ per hour. Fifty percent of the gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy, the number of $100\,W$ lamps that can be lit is (Take $g = 10\,m/s^2$)

$A$ truck and a car are moving with equal velocity. On applying the brakes,both will stop after a certain distance. Which of the following is true?

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.)