The work done by a gas molecule in an isolated system is given by, W… | JEE Main 2021 (24 Feb, Shift 1)

Q48JEE Main 2021 · 24 FEB · SHIFT 1Medium

Applications of Dimensional Analysis

The work done by a gas molecule in an isolated system is

given by, $W = \alpha\beta^2 e^{-\frac{x^2}{\alpha kT}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. $\alpha$ and $\beta$ are constants. Then the dimensions of $\beta$ will be:

Show answer and solution

Answer: (c)

Exponent is dimensionless: $[\alpha] = \dfrac{[x^2]}{[kT]} = \dfrac{L^2}{ML^2T^{-2}} = M^{-1}T^2$ .
$[W] = [\alpha][\beta^2]$ , so $[\beta^2] = \dfrac{ML^2T^{-2}}{M^{-1}T^2} = M^2L^2T^{-4}$ .
$[\beta] = MLT^{-2}$ , so the answer is (c).

Report a mistake

More questions on Applications of Dimensional Analysis

Which of the following equations is dimensionally incorrect? Where t = time, h = height…JEE Main 2021 (31 Aug, Shift 1)
Let force F = Asin (Ct) + Bcos (Dx), where x and t are displacement and time…MHT CET 2020 (16 Oct, Shift 1)
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then…JEE Main 2020 (2 Sep, Shift 2)
The dimension of stopping potential V0 in photoelectric effect in units of Planck's…JEE Main 2020 (8 Jan, Shift 1)
A quantity x is given by ((IFv²)/(WL⁴)) in terms of moment of inertia I, force F…JEE Main 2020 (4 Sep, Shift 2)
If speed V, area A and force F are chosen as fundamental units, then the dimension of…JEE Main 2020 (2 Sep, Shift 1)
A quantity f is given by f = √(hc⁵/G) where c is speed of light, G universal…JEE Main 2020 (9 Jan, Shift 1)
The force ' F ' acting on a body of density ' d ' are related by the relation F = y/√(d)…MHT CET 2019 (2 May, Shift 2)

Applications of Dimensional Analysis question from JEE Main 2021 (24 Feb, Shift 1)

More questions on Applications of Dimensional Analysis