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JEE Main 2019 (9 Jan, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2019 (9 Jan, Shift 2)

Q59JEE Main 2019 · 9 JAN · SHIFT 2Easy

Applications of Dimensional Analysis

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

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Answer: (c)

$[G] = M^{-1}L^3T^{-2}$ , $[h] = ML^2T^{-1}$ , $[c] = LT^{-1}$ .
$[Gh] = L^5T^{-3}$ , and $[c^5] = L^5T^{-5}$ .
$\left[\dfrac{Gh}{c^5}\right] = T^2$ , so $\sqrt{\dfrac{Gh}{c^5}}$ has dimension of time.
So the answer is (c).

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