A particle moves with a velocity $\vec v\, = \,5\hat i – 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be …………… $\mathrm{J} / \mathrm{s}$

The force $F$ acting on a body moving in a circle of radius $r$ is always perpendicular to  the instantaneous velocity $v$. The work done by the force on the body in one complete  rotation is : 

Ball $A$ moving at $12\ m/s$ collides elastically with $B$ at rest as shown. If both balls have the same mass, what is the final velocity of ball $A$ ? ……………… $m/s$

A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

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).