The speed of light ( c), gravitational constant (G) and plank's constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be.

Options

A. `G^(1//2)H^(1//2)C^(-5//2)`
B. `G^(-1//2)h^(1//2)C^(1//2)`
C. `G^(1//2)H^(1//2)C^(1//2)`
D. `G^(1//2)h^(1//2)C^(1//2)`

Answer

A

Explanation

`T propC^qG^b h^c `
`T=K C^a G^b h^c `
`[M^0L^0T^1]=[L^1 T^(-1)]^a[M^(-1)L^(3)T^(-2)]^b`
`[M^(1)L^(2)T^(-1)]^c`
`[M^0L^0 T^1]=[M^(-b+c)L^(a+3b+2c)T^(-a-2b-c)]`
Camparing of dimensions M, L and T
`-b+c =0 rArr a +3b = 2c =0 rArr -1 -2b -c L `
on Solving we get
`a =-5//2b = 1/2 c = 1//2 rArr T C^(-5//2)G^(1//2)h^(1//2)`