Use dimensional analysis to see which of the following expressions is/are NOT allowed if p is a pressure, t is a time, m is a mass, r is a distance, v is a velocity and T is a temperature?

Question

TestHub · Accepted Answer

The argument of a logarithm must be dimensionless.

Use $[p] = [M L^{- 1} T^{- 2}], [t] = [T]$

$[m] = [M], [r] = [L]$

and temperature $[T] = [K]$ .

(A) $[\frac{pt}{m r}] = \frac{[ M L ^{- 1} T ^{- 2} ] [ T ]}{[ M ] [ L ]} = [L^{- 2} T^{- 1}]$ - not dimensionless. Not allowed.

(B) $[\frac{p r t ^{2}}{m}] = [M^{0} L^{0} T^{0}]$ - dimensionless. Allowed.

(C) $[\frac{p r ^{2}}{m t ^{2}}] = [L T^{- 4}]$ - not dimensionless. Not allowed.

(D) $[\frac{p r}{m tT}] = [T^{- 3} K^{- 1}]$ - not dimensionless. Not allowed.

Hence (A), (C) and (D) are not allowed.

Physics - Unit & Dimension Question with Solution | TestHub

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