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:

$A$ body is moving uni-directionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $30 \; m^{3}$ in $15 \; min$. If the tank is $40 \; m$ above the ground, and the efficiency of the pump is $30 \%$, how much electric power (in $kW$) is consumed by the pump?

The power of a crane, which lifts a mass of $1000 \text{ kg}$ to a height of $20 \text{ m}$ in $10 \text{ s}$ is: $(g = 9.8 \text{ ms}^{-2})$

From a waterfall,water is pouring down at the rate of $100 \,kg/s$ on the blades of a turbine. If the height of the fall is $100 \,m$,the power delivered to the turbine is approximately equal to .......... $kW$.

$A$ car of mass $m$ is driven with acceleration $a$ along a straight road against a constant external resistance $R$. When the velocity is $v$,the power of the engine is