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JEE Main 2024 (4 Apr, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2024 (4 Apr, Shift 2)

Q20JEE Main 2024 · 4 APR · SHIFT 2Easy

Applications of Dimensional Analysis

Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

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Answer: (c)

$[G] = [M^{-1}L^3T^{-2}]$ , so $[GM] = [L^3T^{-2}]$ .
$\left[\dfrac{r^3}{GM}\right] = \dfrac{[L^3]}{[L^3T^{-2}]} = [T^2]$ , which matches $T^2$ .
The other options do not give $[T^2]$ .
So the answer is (c) $T^2 = \frac{4\pi^2 r^3}{GM}$ .

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