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