Two bodies of masses $m$ and $4 \,m$ are moving with equal $K.E.$ The ratio of their linear momentums is

Define kinetic energy. Give its unit and dimensional formula and mention works by using it.

Two carts of masses $200\, kg$ and $300 \,kg$ on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the $200 \,kg$ cart travels a distance of $36 \,m$ and stops, then the distance travelled by the cart weighing $300 \,kg$ is ........ $m$

If the momentum of a body is increased by $100\%$, then the percentage increase in the kinetic energy is ............ $\%$

A block moving horizontally on a smooth surface with a speed of $40\, {ms}^{-1}$ splits into two equal parts. If one of the parts moves at $60\, {ms}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be $x: 4$ where $x=..... .$

A shell of mass $200\, gm$ is ejected from a gun of  mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$