Which of the following is equivalent to the unit of power, watt (W)? (1) Nm s⁻² (2) Ns m⁻¹ (3) Nms (4) Nm s⁻¹ (5) Nm² s

What you should connect: power, work, and time

Power is the rate of doing work (or transferring energy). So its unit must be “work per time.”

Convert watts into base mechanical units

By definition, $$1\,\text{W} = 1\,\frac{\text{J}}{\text{s}}.$$ Also, $$1\,\text{J} = 1\,\text{N}\cdot \text{m}.$$ Substitute $\text{J}=\text{N m}$ into the watt definition: $$1\,\text{W} = 1\,\frac{\text{N m}}{\text{s}} = 1\,\text{N m s}^{-1}.$$ So option (4) matches.

Quick elimination check on the other options

• (1) $\text{N m s}^{-2}$ is $\text{(N m)}/\text{s}^2 = \text{J}/\text{s}^2$, not power.
• (3) $\text{N m s}$ is $\text{J}\cdot \text{s}$, not $\text{J}/\text{s}$.
• (2) $\text{N s m}^{-1}$ and (5) $\text{N m}^2\text{s}$ do not reduce to $\text{N m}/\text{s}$.