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^(-12)G^(1//2)h^(1//2)`

Answer

C

Explanation

Let `[M] =K.c^(x)G^(y)h^(x)," "[m]=[LT^(-1)]^(x).[M^(-1)L^(3)T^(-2)]^(y).[ML^(2)T^(-1)]^(2)`
`[ML^(@)T^(@)]=M^(-y+z).L^(x+3y+2z).T^(-x-2y-z)`
compare powers of M,L and T on both sides
`x=1/2,y=-1/2,z=1/2`
`:.` [Mass in new system] `=c^(1//2),G^(-1//2),h^(1//2)`