The Energy (E), Angular momentum (L) and Universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Plank's constart (h) is

Options

A. Zero
B. -1
C. `5/3`
D. 1

Answer

A

Explanation

Planck's constant , `h = E^(a)L^(b)I^(c )`(a,b,c- constants)
According to the principle of homogeneity of dimensions,
`h = [ML^(2)T^(-1)], E = [ML^(2)T^(-2)], L = [ML^(2)T^(-1)], G = [M^(-1)L^(3)T^(-2)]`
On substituing the values of h,E,L and G in equation,
`[ML^(2)T^(-1)] = [ML^(2)T^(-2)]^(a)[ML^(2)T^(-1)]^(b)[M^(-1)L^(3)T^(-2)]^(c)`
`M = M^(a+b-c) implies a+b-c = 1` ...(1)
`L^(2) = L^(2a+2b+3c) implies 2a+2b+3c = 2` ...(2)
`T^(-1) = T^(-2a-b-2c) implies 2a+b+2c = 1` ...(3)
On solving equations (1),(2) and (3), we get,c = 0