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Expression for time in terms of G (unive...

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

A

`sqrt((c^3)/(Gh))`

B

`sqrt((hc^5)/(G))`

C

`sqrt((Gh)/(c^5))`

D

`sqrt((Gh)/(c^3))`

Text Solution

Verified by Experts

The correct Answer is:
C
`t = k cdot G^(x) h^*y cdot c^(z) , [t] = [k] [(Fd^2)/(m_1m_2)] [E/v]^(y) [c]^(z)`
`[(MLT^(-2)L^(-2))/(M^2)]^(x) [(ML^2T(-2))/(T^(-1)]^(y) - [LT^(-1)]^(z) = M^(-x) L^(3x)T^(-2x) M^(y)L^(2y) T^(-y)L^(z) T^(-z)`
`[t] = M^(y - x) L^(3x + 2y + z) T^(-2x - y - z)`
Comparing `y = x, 3x + 2y + z = 0`
`implies z = -5x and -3x + 5x = 1 implies x = 1/2 implies y = 1/2 implies z = (-5)/2`
So `t prop sqrt(GH)/(c^5)`.
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