First slide

Dimensions of physical quantities

Question

A quantity $f$ is given by $f = \sqrt{\frac{h c^{5}}{G}}$ where c is speed of light, G universal gravitational constant and h is the Planck’s constant . Dimensions of f is that of:

Moderate

A

energy
B

momentum
C

area
D

volume

Solution

$\begin{array}{l} f = \sqrt{\frac{h c^{5}}{G}} \\ w e k n o w, d i m e n s i o n o f \\ [h] = [M^{1} L^{2} T^{- 1}], [c] =[M^{0} L^{1} T^{- 1}], [G] =[M^{- 1} L^{3} T^{- 2}] \\ ∴ f = \sqrt{\frac{[M^{1} L^{2} T^{- 1}] \times {[M^{0} L^{1} T^{- 1}]}^{5}}{[M^{- 1} L^{3} T^{- 2}]}} = [M^{1} L^{2} T^{- 2}] \\ w h i c h i s t h e d i m e n s i o n o f e n e r g y . \end{array}$

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