Question

Ten liter of water per second is lifted from a well through $10m$ and delivered with a velocity of $10m{s}^{-1}$ . If $g=10m{s}^{-2}$, then the power of the motor is

• A. $1kW$
• B. $1.5kW$
• C. $2kW$
• D. $2.5kW$

Answer 1

The correct option is B

$1.5kW$

Step 1: Given data

Depth of the well, $h=10m$

Velocity by which water is delivered, $v=10m{s}^{-1}$

Time, $t=1s$

Acceleration due to gravity, $g=10m{s}^{-2}$

Step 2: Calculating power of the motor

The total energy can be calculated by adding kinetic and potential energies.

Kinetic energy is determined by the expression $\frac{1}{2}\mathrm{m}{v}^2$, where $\mathrm{m}$ is the mass and $v$ is the velocity of the body.

Potential energy is determined by the expression $\mathrm{m}gh$, where $g$ is the acceleration due to gravity and $h$ is the height.

One liter of water is equal to $1kg$.

Power $P$ can be calculated by the expression below:

$\begin{array}{rcl}P& =& \frac{\mathrm{m}gh+{\displaystyle \frac{1}{2}}\mathrm{m}{v}^2}{t}\\ & =& \frac{m}{t}\left[gh+\frac{v^2}{2}\right]\\ & =& \frac{10kg}{1s}\left[10m{s}^{-2}\times 10m+\frac{{10}^{2}m{s}^{-1}}{2}\right]\\ & =& 10\left(100+50\right)\\ & =& 1500W\\ & =& 1.5kW\end{array}$

The power of the motor is $1.5kW$

Hence, option (b) is correct.