Question

The unit of power is
(A) Watt per second
(B) Joule
(C) Kilo joule
(D) Watt

Answer 1

Hint: In this question, we are asked to choose appropriately from the options the correct unit of power. Consider the definition of power, from there you can get an idea of what is power and then you can easily find the unit of power. Here, in order to proceed, consider a force which is acting on a block and derive relevant quantities which can be obtained from the force.

Complete answer:
Let us consider a block which is lying on a frictionless floor. Let us apply a horizontal force $F$ on the block parallel to the surface of the floor. As the floor is frictionless, no resistive force can act on the block corresponding to the force $F$. As a result, the block will start to move according to Newton's 2nd law.

So, if the block moves an infinitesimal distance equal to \[dx\] (obviously in the direction of the force) in a time interval equal to $dt$, then we say that a work is done by the force on the block and its magnitude is equal to force times the displacement, $dW = Fdx$, where $dW$ is the infinitesimal work done. As work is energy, its unit is joule.

If we write the velocity $v$ of the block as $\dfrac{{dx}}{{dt}}$, we have $dx = vdt$. Now, we have,
$dW = Fvdt
\Rightarrow \dfrac{{dW}}{{dt}} = Fv$$...\left( 1 \right)$
This term is defined as the power delivered to the block by the force $F$. So, we have power $P = \dfrac{{dW}}{{dt}}$. As you can see that the unit of power is joule per second which is also denoted as watt.

Hence, the unit of power is watt.Option (D) is correct.

Note:You should always keep in mind that the power is defined as the energy transferred per unit time, from there you can simply tell the unit of power. Also remember the way in which we found out the unit of power. Power can be joule per second and it also can be Newton metre per second, as you can see in the equation $\left( 1 \right)$.