Q: If c is the velocity of light, h is Planck’s constant and G is Gravitational constant are taken as fundamental quantities. Them the dimensional formula of mass is

Sol. c = [LT^{-1} ] …(i)

h = [ML^{2} T^{-1} ] …(ii)

G = [M^{-1} L^{3} T^{-2} ] …(iii)

Solving (ii) and (iii)

h/G = [(ML^{2} T^{-1})/(M^{-1} L^{3} T^{-2} )]

=[M^{2} L^{-1} T^{1} ]

Substituting (i) in above

h/G = M^{2}/c

⇒ [M] = [h^{1/2} G^{-1/2} c^{1/2} ]

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