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JEE Main 2024 (30 Jan, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2024 (30 Jan, Shift 2)

Q24JEE Main 2024 · 30 JAN · SHIFT 2Easy

Applications of Dimensional Analysis

If mass is written as $m = k\mathrm{c}^{\mathrm{P}}G^{-1/2}h^{1/2}$ then the value of $P$ will be: (Constants have their usual meaning with $k$ a dimensionless constant)

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Answer: (c)

$[G^{-1/2}] = M^{1/2}L^{-3/2}T^{1}$ , $[h^{1/2}] = M^{1/2}L^{1}T^{-1/2}$ .
Product: $M\,L^{-1/2}T^{1/2}$ ; with $[c^P] = L^PT^{-P}$ the total is $M\,L^{P-1/2}T^{1/2-P}$ .
For pure mass, $P - \frac{1}{2} = 0$ , so $P = \frac{1}{2}$ .
So the answer is (c) 1/2.

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