If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

Step-by-step solution

Let, aligned M & =C^a h^b G^c ML ^0 ~T ^0 & = [ LT ⁻¹ ]^a [ ML ^2 ~T ⁻¹ ]^ b [ M ⁻¹ ~L ^3 ~T ⁻² ]^ a aligned where, h= Energy Frequency aligned & = [ ML ^2 ~T ⁻² ] [ T ⁻¹ ] = [ ML ^2 ~T ⁻¹ ] C & = Metre Second = [ LT ⁻¹ ] G & = Force (distance) (mass) & = [ MLT ⁻² ] [ L ^2 ] [ M ^2 ] = [ M ⁻¹ ~L ^3 ~T ⁻² ] aligned Comparing the coefficients M, L, T , of both sides we get array l b-c=1 a+2 b+3 c=0 -(a+b+2 c)=0 array Solve the Eqs. (ii), (iii) and (iv), we get a= 1 2 , b= 1 2 , c=- 1 2 So, M=h^ 1 / 2 C^ 1 / 2 G^ -1 /