If velocity of light c, planck's constant h and gravitational constnat G are taken as fundamental quantities then the dimensions of the length will be

Explanation

We know , (V) `=[LT^(-1)],[h] = [ML^2 T^(-1)]`
`[G] = [M^(-1)L^3 T^(-2)]`
Let L= `V^a h^b G^c`
`M^0 L^1 T^0 =(LT^(-1))^a (ML^(-1))^b (M^(-1) L^3 T^(-2))^c`
comparing the powers of M, L, T both sides
b-c =0 ……………(1)
a+2b +3c =1 ...............(2)
-a-b-2c =0 ...............(3)
on solving (1), (2),(3) ..............
On solving (1),(2) ,(3)
we get `a=- 3/2 ,b =1/2 , c=1/2`
`L = V^(-3//2) h^(1//2) G^(1//2)`