Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\, m/s$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is .............. $\mathrm{m}/ \mathrm{s}$

Two identical $5\,\,kg.$  blocks are moving with same speed of $2\,\,m/s$  towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$

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 $t = 4 \,sec.$ ............... $\mathrm{J}$

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{\upsilon }$  where $K$ is a constant. The work done by this force in time $t$ is

A force acts on a $3.0\ g$ particle in such a way that the position of the particle as a function of time is given by:

$x = 3t - 4t^2 + t^3$ 

Where $x$ is in metres and $t$ is in seconds. The work done during the first $4\ s$ is ................. $\mathrm{mJ}$

The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at