Question

A 12 HP motor has to be operated 8 hours/day. How much will it cost at the rate of 50 paise/kWh in 10 days
A. \[Rs350\]
B. \[Rs358\]
C. \[Rs375\]
D. \[Rs397\]

Answer 1

Hint: We will use the formula for power and energy. First we can calculate power with the given values. After calculating power, energy can be calculated by substituting the values in the formula. Convert the unit of power, time and cost.

Formula used: Energy = Power $\times$ Time

Complete answer:
In an electric motor, electric power is converted into mechanical power. Mechanical power is generally defined as kilowatts or horsepower. Therefore horsepower can also be defined as work done per unit time.
Given – Power = 120 HP
               Time = 8 hours/day
               Cost = 50 paise/kWh
               No. of days = 10
We know, 1HP = 746 watt
Therefore 12HP = (12 $\times$ 746) watt
Energy is the amount of work done or the capacity for doing any work. The energy used by the motor has been calculated. Therefore total energy used is given by
Energy = Power $\times$ Time
Time = \[8hour=8\times 3600\sec \]
For 10 days,
  \[\begin{align}
  & =12\times 746\times 8\times 3600\times 10 \\
 & =2578176000J \\
\end{align}\]
It is given that 50 paise/kWh costs in 10 days for the motor. So cost per unit energy can be calculated as
 \[Cost=\dfrac{0.5}{{{10}^{3}}\times 3600}Rs/J\]
Therefore total cost is given by
 \[\begin{align}
  & Total\cos t=2578176000\times \dfrac{0.5}{{{10}^{3}}\times 3600} \\
 & =Rs358
\end{align}\]
Hence, for operating a motor for 10 days Rs. 358 will be the cost at rate of 50 paise/kWh.

Therefore option B is correct.

Note:
Units should be taken care of. The unit of horsepower is changed to watt. Likewise the unit of time and rupee has also been changed. Work, energy and power is an important concept and all these forces result in kinetic energy.