Question

Which of the following is not the unit of surface tension ?

• A. $\frac{N}{m}$
• B. $\frac{J}{m^2}$
• C. $\frac{Kg}{s^2}$
• D. $\frac{Watt}{m}$

Answer 1

Answer: (D)

As we know, surface tension,
$S=\frac{\text{ force }}{\text{ length }}=\frac{F}{l}$
Hence, its SI unit is $\frac{N}{m}$.
So, option (a) is unit of surface tension.
Again, option (b) $\frac{\text{ joule }}{(\text{ metre }{)}^2}\cong \frac{\text{ energy }}{(\text{ length }{)}^2}$
$=\frac{\text{ force }\times \text{ length }}{(\text{ length }{)}^2}=\frac{\text{ force }}{\text{ length }}=\frac{F}{l}$
In terms of SI unit, it will be $\frac{N}{m}$, hence it is also
equal to surface tension.
Again, option (c) $\frac{kg}{s^2}\approx \frac{\text{ mass }}{(\text{ time }{)}^2}$
But $\frac{\text{ energy }}{(\text{ length }{)}^2}=\frac{F\times s}{s^2}=\frac{m\times a\times s}{s^2}$
$=m\times \frac{\text{ distance }}{(\text{ time }{)}^2}\times \frac{1}{\text{ distance }}=\frac{kg}{s^2}=\frac{F}{l}$
Hence, option (c) also equivalent to surface tension.
But, option (d) $=\frac{\text{ watt }}{\text{ metre }}=\frac{\text{ power }}{\text{ mass }}$
$=\frac{\text{ force }\times \text{ distance }}{\text{ mass }}=\frac{N-m}{kg}$
cannot be equal to surface tension.