Two men have a weight ratio of $5 : 3$. If the ratio of the time taken by them to climb stairs is $11 : 9$,find the ratio of their power.

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

$A$ force applied by an engine on a train of mass $2.05 \times 10^6 \ kg$ changes its velocity from $5 \ m/s$ to $25 \ m/s$ in $5 \ minutes$. The power of the engine is (in $MW$)

An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

$A$ man $M_1$ of mass $80 \ kg$ runs up the stairs with a box in $15 \ s$. Another man $M_2$ of the same mass $80 \ kg$ runs up the same stairs with the same box in $20 \ s$. Find the ratio of the power generated by them.

An electric pump is used to fill an overhead tank of capacity $9\,m^3$ kept at a height of $10\,m$ above the ground. If the pump takes $5\,minutes$ to fill the tank by consuming $10\,kW$ power,the efficiency of the pump should be : ............... $\%$ (Take $g = 10\,m/s^2$)