If c is the velocity of light, h is Planck’s constant and G is Gravitational constant are taken as fundamental quantities…

by Jha

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 = [ML² T^-1 ] …(ii)

G = [M^-1 L³ T^-2 ] …(iii)

Solving (ii) and (iii)

h/G = [(ML² T^-1)/(M^-1 L³ T^-2 )]

=[M² L^-1 T¹ ]

Substituting (i) in above

h/G = M²/c

⇒ [M] = [h^1/2 G^-1/2 c^1/2 ]