Which one of the following physical quantities has the same dimensions as that of Planck’s constant h?
Linear momentum
Angular momentum
Force
Potential energy
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CDS-2 – 2016
– Let’s check the dimensions of the given options:
– Linear momentum (p = mv): [M] * [LT⁻¹] = [MLT⁻¹].
– Angular momentum (L = Iω or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML²] * [T⁻¹] or [L] * [MLT⁻¹] = [ML²T⁻¹].
– Force (F = ma): [M] * [LT⁻²] = [MLT⁻²].
– Potential energy (e.g., mgh): [M] * [LT⁻²] * [L] = [ML²T⁻²].
– Comparing the dimensions, angular momentum [ML²T⁻¹] has the same dimensions as Planck’s constant [ML²T⁻¹].