Kevin S. Huang

2012: Problem 22

Topic: Other
Concepts: Dimensional analysis

Solution:

To figure out the base units of power, recall the equation $P=Fv$ . Taking the units of both sides,

[P]=[F][v]=[F]\mathrm{\frac{m}{s}}

To figure out the base units of force, recall the equation $F=ma$ . Taking the units of both sides,

[F]=[m][a]=\mathrm{kg \cdot \frac{m}{s^2}}

Substituting this in the previous equation,

[P]=\mathrm{kg \cdot \frac{m^2}{s^3}}

Since by definition $[P]=\mathrm{W}$ , we have

\mathrm{W}=\mathrm{\frac{kg \cdot m^2}{s^3}}

Finally,

\mathrm{\frac{W}{m^2}}=\mathrm{\frac{kg}{s^3}}

so the answer is A.