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^(-3//2)`
D. `G^(1//2) h^(1//2) c^(1//2)`

Answer

A

Explanation

(1) `t prop G^(a) h^(b) c^(c )`
`T prop [M^(-1) L^(3) T^(-2)]^(a) [ML^(2) T^(-1)]^(b) [LT^(-1)]^(c )`
`M^(0) L^(0) T^(1) prop M^(a + b) L^(3a + 2b + c) T^(-2a - b -c)`
`-a + b = 0, 3a + 2b + c = 0, - 2a - b - c =1`
`a = (1)/(2), b = (1)/(2), c = - (5)/(2)`
`t prop G^(1//2) h^(1//2) c^(/5//2)`