After on head on elastic collision between two balls of equal masses , one is observed to  have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are

Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a  spring and are resting on a horizontal surface. The blocks are pulled apart so as to strech  the spring and then released. The ratio of $K.E.s$ of both the blocks is

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

If $F = 2x^2 -3x -2$, then choose correct option

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

A body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction ............. $\mathrm{J}$  $(g = 10\, m/s^2)$