If `'G''c'` and `'h'` are usual constants of physics, the unit of time is expressed as :

Options

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

Answer

B

Explanation

`T=G^(x)c^(y)h^(z)`
`M^(0)L^(0)T^(1)=(M^(-1)L^(3)T^(-2))^(x)xx(L^(1)T^(-1)]^(y)xx[ML^(2)T^(-1)]^(z)`
`=M^(-x-y)L^(3x+y+2z)T^(-2x-y-z)`
`-x+z=0 3x+y+2z=0-2x-y-z=1`
`x=z3z+2z=-y-2z-z=1+y`
`5z=-y-3z=y+1`
`5z=3z+1y=-3z-1`
`x=1//2z=1` or `z=1//2y=-5//2`
or `T=G^(1//2)c^(-5//2)h^(1//2)`
`sqrt((hG)/(c^(5)))`
Hence correct choice is `(b)`.