Units & Dimensions

JEE Main level, single correct, medium

95 of 149

Question 95 of 149

Identify the pair of physical quantities that have same dimensions:

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Answer: (A) Velocity gradient and decay constant

Decay constant is measured per unit time, λ=s−1\lambda ={s}^{-1}
So, its dimension is [λ]=[T−1]\left[\lambda \right]=\left[{T}^{-1}\right]
We know velocity gradient is defined as rate of change in velocity per unit of distance. So, dimension of velocity gradient is
[dvdx]=[L1T−1][L1]=[T−1]\left[\dfrac{dv}{dx}\right]=\dfrac{\left[{L}^{1}{T}^{-1}\right]}{\left[{L}^{1}\right]}=\left[{T}^{-1}\right]

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