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 force acts on a $3\, gm$ 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 $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is ................. $\mathrm{mJ}$

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :

A $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N\, m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $\mathrm{m}/ \mathrm{s}$   $(g = 10\, m/s^2$)

A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

$A$ ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is .................. $\mathrm{sec}$