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JEE Main 2022 (28 Jun, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2022 (28 Jun, Shift 2)

Q38JEE Main 2022 · 28 JUN · SHIFT 2Medium

Applications of Dimensional Analysis

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_2 = \frac{n}{m^2}v_1$ and $a_2 = \frac{a_1}{mn}$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are:

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Answer: (a)

$v = L/T$ and $a = L/T^2$ , so $T = v/a$ and $L = v^2/a$ .
$T_2 = \dfrac{v_2}{a_2} = \dfrac{n/m^2}{1/(mn)}\,T_1 = \dfrac{n^2}{m}T_1$ .
$L_2 = \dfrac{v_2^2}{a_2} = \dfrac{n^2/m^4}{1/(mn)}\,L_1 = \dfrac{n^3}{m^3}L_1$ .
So the answer is (a).

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