Question

The rate of doing work is called ………..
A. Power
B. Energy
C. Acceleration
D. Velocity

Answer 1

Hint: Understand the concept of work done and obtain the equation related to it. Then find the work done per unit time or the rate of work done to find what it means. Try to break them in terms of fundamental quantities. This way also we can find our answer.

Complete Step-by-Step solution:
Work can be defined as the energy required to move an object by a distance by applying a force. It can be expressed as,
$\text{work done = force applied }\times \text{ distance moved }$
The SI unit of force is Newton and the unit of distance is meter.
In symbolic form we can write,
$W=F\times d$
In vector form we can write,
$\begin{align}
  & W=\vec{F}.\vec{d} \\
 & W=Fd\cos \theta \\
\end{align}$
where, $\theta $ is the angle between the direction of force and the direction of the movement of the object.

The SI unit of work done is joule.
Now, the rate of work done means the amount of work done per unit time.
Now, power can be defined as the amount of energy Transferred per unit time. Energy transferred is the same as the work done on the object.
So, power can be defined as the amount of work done per unit time or the rate of doing work.
The unit of power is watt.
It can be expressed by the equation,
$P=\dfrac{W}{t}$
The correct option is (A).
Additional information: The dimension of work done is given as, $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}} \right]$
The dimension of power is given as, $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-3}} \right]$

Note: The power is also defined as the amount of energy transferred per unit time. So, we can also express power as,
$P=\dfrac{\Delta E}{\Delta t}$
We can also get this answer by dimensional analysis. We have both the dimension of work and power. If we see the dimensions, the dimension of power can be obtained by dividing the dimension of work by dimension of time. And we are asked to find the rate of doing work which can only be power.