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

Asked in JEE Main 9th Jan 2nd Shift 2019 · Expressing a quantity in new base units

Answer: (3) √(Gh)/(c⁵)

Step-by-step solution

Given: G=[M⁻¹L³T⁻²], h=[ML²T⁻¹], c=[LT⁻¹].

Gh=[L⁵T⁻³], in which the mass has already cancelled.

(Gh)/(c⁵)=([L⁵T⁻³])/([L⁵T⁻⁵])=[T²].

Taking the square root gives a time, so t∝√(Gh)/(c⁵), the Planck time.

Why the other options are wrong

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