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  • The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as fundamental units in a system. The dimensions of the time in the new system should be<div class='qn

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

Option: 1

G^{\frac{1}{2}}h^{\frac{1}{2}}c^{\frac{-5}{2}}


Option: 2

G^{\frac{-1}{2}}h^{\frac{1}{2}}c^{\frac{1}{2}}


Option: 3

G^{\frac{1}{2}}h^{\frac{1}{2}}c^{\frac{-3}{2}}


Option: 4

G^{\frac{1}{2}}h^{\frac{1}{2}}c^{\frac{1}{2}}


Answers (1)

best_answer

\\T\propto c^a G^b h^d \\T= k c^a G^b h^d \\\left[T \right ] = [k] [c]^a [G]^b [h]^d \\\left[T \right ] =[LT^{-1}]^a[M^{-1}L^{3}T^{-2}]^b[ML^2T^{-1}]^d

By comparing the power of M, L & T.

\\-b + d = 0 \Rightarrow b =d \;\;\; -(1) \\a+3b+2d = 0\;\;\;-(2) \\-a-2b-d=1\;\;\;-(3)

By solving (1), (2) and (3)

a = \frac{-5}{2}\;\;\;b=d =\frac{1}{2}

T = kG^{\frac{1}{2}}h^{\frac{1}{2}}c^{\frac{-5}{2}}

Posted by

Ritika Kankaria

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