If the velocity of light `(c )` , gravitational constant `(G)` , and Planck's constant `(h)` are chosen as fundamental units , then find the dimensions of mass in new system.

Options

A. `c^((1)/(2))G^((1)/(2))h^((1)/(2))`
B. `c^((1)/(2))G^((1)/(2))h^((-1)/(2))`
C. `c^((1)/(2))G^((-1)/(2))h^((1)/(2))`
D. `c^((-1)/(2))G^((1)/(2))h^((1)/(2))`

Answer

C

Explanation

Let `mpropC^xG^yh^z`
By substituting the following dimension:
`[C]=LT^-1`,[G]=[M^-1L^3T^-2]` and `[h]=[ML^2T^-1]`
Now comparing both sides we will get
`x=(1)/(2)`,`y=(-1)/(2)`,`z=(+1)/(2)`
so `mpropc^((1)/(2))`G^((-1)/(2))`h^((1)/(2))`