Question

If power $(P)$, surface tension $(S)$ and Planck’s constant $(h)$ are arranged so that the dimensions of time in their dimensional formulae are in ascending order, then which of the following is correct ?

• A. $P$, $S$, $h$
• B. $P$, $h$, $S$
• C. $S$, $P$, $h$
• D. $S$, $h$, $P$

Answer 1

Answer: (A)

Power $=\frac{\text{Work}}{\text{Time}}$
$\therefore \left[P\right]=\frac{\left[ML^{2}T^{-2}\right]}{\left[T\right]}=\left[ML^{2}T^{-3}\right]$
Surface tension $=\frac{\text{Force}}{\text{Length}}$
$\therefore \left[S\right]=\frac{\left[MLT^{-2}\right]}{\left[L\right]}=\left[ML^{0}T^{-2}\right]$
Planck's constant
$=\frac{\text{Energy}}{\text{Frequency}}$
$\therefore \left[h\right]=\frac{\left[ML^{2}T^{-2}\right]}{\left[T^{-1}\right]}=\left[ML^{2}T^{-1}\right]$
The ascending order of dimensions of time in their dimensional formulae is $P$, $S$, $h$.