Question

The amount of energy consumed by a 10 hp water pump in 30 minutes to lift water to the overhead tank is:
A) $26.656 \times {10^6}$ J.
B) $0.8949 \times {10^6}$ J.
C) $53.712 \times {10^6}$ J.
D) $13.428 \times {10^6}$ J.

Answer 1

When we use a water pump to lift water to an overhead tank then we are consuming energy which will be equal to the amount of power consumed by the lift in a minute and the number of minutes we use the pump to lift water. In this particular problem, we have to calculate the amount of energy consumed. This can be easily done by using the energy formula, $Energy = Power \times Time$. By using this we can get our desired result.

Formula Used: $Energy = Power \times Time$

Complete step by step answer:
Energy can be defined in physics as the ability to do work. This can be easily done by using the energy formula,
$Energy = Power \times Time$.
Thus, when we use a water pump to lift water to an overhead tank, we are consuming energy which will be equal to the amount of power consumed by the lift in a minute and the number of minutes we use the pump to lift water.
As the pump is 10 hp then we can say that the Power= 10hp. Also, the time frame for which the pump was used is 30 minutes thus we can write Time= 30 min.
Now, $Energy = Power \times Time$.
Putting the values given in the question we get,
$Energy = 10hp \times 30\min$
Also, 10hp =10*746W as 1hp=746W and 30min=30x60=1800sec.
Thus, the equation can be rewritten as,
$Energy = 746 \times 1800$ J.
Calculating we get $Energy = 13428000$ J.
This can be written in scientific terms as,
$Energy = 13.428 \times {10^6}$J.

Thus, the option (D) is the right answer.

Note:
This problem is a very straight forward answer. The only thing needed is the formula for Energy. If we remember the formula for energy then we can put the other terms which are available in the question and we can get the answer. We just remember one thing. We have to convert the given terms into their SI format or else we will never be able to arrive at the given answer.