If the speed of light `c(=3xx10^(8) m//s)`, Planck's contant `h(=6.6xx10^(-34) J-s)` and gravitational constant `G(=6.67xx10^(-11)MKS" units")` are chosen as the fundamental quantities, find out the dimensions and value of units of (a) mass, and (b) time in this system.

Answer

`Q_(m)=(ch//G)^(1//2) ~ 10^(-7) kg`,
`Q_(t)=(Gh//c^(5))^(1//2)~ 10^(-42) s`

Explanation

`Q=f(a, c, h)`
`[M]=[M^(-1)L^(3)T^(-2)]^(x)[LT^(-1)]^(y)[ML^(2)T^(-1)]^(z)`
Equating the exponents of similar quantities
`-x+z=1`
`3x+y+2z=0`
`-2x-y-z=0`
`x=-1/2" "," "y=1/2" "," "z=1/2`
`Q = ((cn)/a)^(1//2)`