$A$ pump on the ground floor can pump up water to fill a tank of volume $30 \ m^3$ in $15 \ minutes$. If the tank is $40 \ m$ above the ground and the efficiency of the pump is $30\%$,then the electric power consumed by the pump is ....... $kW$.

$A$ pump is required to lift $1000 \, kg$ of water per minute from a well of depth $10 \, m$ and eject it with a speed of $10 \, m/s$. The horsepower of the engine needed is: (Assume $g = 10 \, m/s^2$)

$A$ block of mass $50 \,kg$ is pulled with a constant speed of $4 \,ms^{-1}$ across a horizontal floor by an applied force of $500 \,N$ directed $30^{\circ}$ above the horizontal. The rate at which the force does work on the block in watt is

$A$ 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 $.............. \ W$.

$A$ body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to

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: