Question

Which one of the following is ‘watt’?

• A. $kgm{s}^{-2}$
• B. $Nm{s}^{-2}$
• C. $kg{m}^2{s}^{-3}$
• D. $Nm{s}^{-1}$

Answer 1

Answer: (C), (D)

$Nm{s}^{-1}$

The explanation for the correct options:

D. $Nm{s}^{-1}$

1. Watt is the SI unit of Power
2. The time rate of doing work is termed as power (P).
3. Power SI unit is Joule per second or J/s or Watt.

$$\begin{gathered} 1W=1J{s}^{-1} \\ =1N\times 1m\times 1s^{-1} \\ =1Nm{s}^{-1} \end{gathered}$$

C. $kg{m}^2{s}^{-3}$

It is also an SI unit of power that is a Watt.

$$\begin{gathered} 1W=1J{s}^{-1} \\ =1N\times 1m\times 1s^{-1} \\ =1Nm{s}^{-1} \\ =1kg\times m{s}^{-2}m{s}^{-1} \\ =1kg{m}^2{s}^{-3} \end{gathered}$$

The explanation for the incorrect options:

A. $kgm{s}^{-2}$

It is the SI unit of Force.

B. $Nm{s}^{-2}$

It is not the dimensional of Watt as it is force multiplied by acceleration.

Options C, and D are the correct option.

Thus, $1watt=1kg{m}^2{s}^{-3}=1Nm{s}^{-1}$