Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in  second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ ............... $\mathrm{J}$

A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$

A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is

A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ 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).

A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is