Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

Options

A. `sqrt((hc^5)/(G))`
B. `sqrt((Gh)/(c^3))`
C. `sqrt((c^3)/(Gh))`
D. `sqrt((Gh)/(c^5))`

Answer

D

Explanation

`[t]=[G]^(a)[h]^(b)[c]^(d)`
`[T].= [M^(-1)L^(3)T^(-2)]^(a)[M^(1)L^(2)T^(-1)]^(b)[L^(1)T^(-1)]^(d)`
`[T].= [M^(-a+b)L^(3a+2b+d)T^(-2a-b-d)]`
`-a+b=0" ""…………."(i)`
`3a+2b+d=0" ""………."(ii)`
`2a+b+d= -1" ""……….."(iii)`
From eqaution (i) (ii) and (iii) we get,
`a=(1)/(2), b=(1)/(2),d=(5)/(2)`
`t=G^(1/2)h^(1/2)c^(-5/2)= sqrt((Gh)/(c^5))`