Question

1 Megawatt \[ = a\], 1 Horsepower \[ = b\]
A. \[a = {10^3}W\], \[b = 1.34W\]
B. \[a = {10^6}W\], \[b = 746W\]
C. \[a = {10^6}j\],\[b = 0W\]
D. \[a = 10W\], \[b = {10^3}W\]

Answer 1

Hint:Power:- Power is a measure of energy transferred per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity also. Power is a scalar quantity.
S.I. Unit of Power is watt.

Complete step by step solution:
$watt = \dfrac{{Joule}}{{\sec }}$
Mega is a unit prefix in metric systems of units denoting a factor of one million $\left( {{{10}^6}} \right)$ or $1000000$.
Horsepower $\left( {hp} \right)$ is also a unit of power.Horsepower is a unit of measurement of power, or the rate at which work is done, generally it is used in power measurement of engine or motor. There are many different standards and types of horsepower. Horsepower was invented based on some assumptions. It was used in the initial industrial age and now it is used but it is not accepted as an SI unit.
Watt is defined as 1 J energy transferred in 1s. It is a standard SI unit of power named after Sir James Watt.
$Mega = {10^6}$
$1Megawatt = {10^6}watt{\text{ }}or 1000000 watt$
$1Horsepower\left( {hp} \right) = 746watt$(Standard value)
So option B is correct.

Note: Horsepower $\left( {hp} \right)$ and Watt $\left( w \right)$ both are the standard units of power. Horsepower was given by James Watt. Horsepower is not the value of energy which a horse generates in one time. Because a horse can generate up to $15hp$ in one time. So it is wrong to describe it with power generated by horse at one time. This unit was further standardized with SI unit $watt$.