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)

P, S, h

Answer 2

Power $= \frac{Work}{Time}$

$\lbrack P\rbrack = \frac{\lbrack ML^{2}T^{- 2}\rbrack}{\lbrack T\rbrack} = \lbrack ML^{2}T^{- 3}\rbrack$

Surface tension$= \frac{Force}{Length}$

$\lbrack S\rbrack = \frac{\lbrack MLT^{- 2}\rbrack}{\lbrack L\rbrack} = \lbrack ML^{0}T^{- 2}\rbrack$

Planck’s constant $= \frac{Energy}{Frequency}$

$\lbrack h\rbrack = \frac{\lbrack ML^{2}T^{- 2}\rbrack}{\lbrack T^{- 1}\rbrack} = \lbrack MT^{2}T^{- 1}\rbrack$

The ascending order of dimensions of time in their dimensional formulae is P,S,h.