A sphere of mass $0.1\,\,kg$  is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table. If the impact is elastic, then the kinetic energy of the block after the collision is ............. $\mathrm{J}$

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 long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2s$ will be ............. $\mathrm{m}/ \mathrm{s}$

A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ........... $\%$