The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}$,which are capable of raising $300 \ kg$ of water in $5 \ minutes$ and $50 \ kg$ of water in $2 \ minutes$ respectively from a well of $100 \ m$ depth. The value of $x$ is:

$A$ car of mass $2000 \ kg$ is lifted by a crane through a distance of $30 \ m$ in $1 \ minute$. $A$ second crane does the same in $2 \ minutes$. The power supplied by each crane is respectively:

$A$ body of mass $1\, kg$ begins to move under the action of a time-dependent force $\overrightarrow{F} = (2t\hat{i} + 3t^2\hat{j})\, N$,where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$ axes. What power will be developed by the force at time $t$?

An object of mass $m$ is projected with an initial velocity $u$ at an angle $\theta$ with the horizontal. What is the average power delivered by gravity in reaching the highest point?

$A$ weight lifter lifts $300 \ kg$ from the ground to a height of $2 \ m$ in $3 \ s$. The average power generated by him is $... \ W$.

$A$ machine gun fires $300$ bullets per minute, each with a velocity of $500 \,ms^{-1}$. If the mass of each bullet is $4 \,g$, the power of the machine gun is: (in $\,kW$)