The frequency ( ν) of an oscillating liquid drop may depend upon radius ( r) of the drop, density ( ρ) of liquid and the surface tension (s) of the liquid as ν = raρbsc. The values of a, b and c respectively are (a) (3/2, 1/2, -1/2) (b) (-3/2, -1/2, 1/2) (c) (3/2, -1/2, 1/2) (d) (-3/2, 1/2, 1/2)

Answer: (b). [ν] = T⁻¹, [r] = L, [ρ] = ML⁻³, [s] = MT⁻². M: b + c = 0; L: a - 3b = 0; T: -2c = -1. c = 1/2, b = -1/2, a = -3/2. So the answer is (b) (-3/2, -1/2, 1/2).

The frequency ( ν) of an oscillating liquid drop may depend upon… | JEE Main 2023 (24 Jan, Shift 2)

Q10JEE Main 2023 · 24 JAN · SHIFT 2Medium

Molecular Theory & Factors

The frequency ( $\nu$ ) of an oscillating liquid drop may depend upon radius ( $r$ ) of the drop, density ( $\rho$ ) of liquid and the surface tension (s) of the liquid as $\nu = r^{a}\rho^{b}s^{c}$ . The values of a, b and c respectively are

Show answer and solution

Answer: (b)

$[\nu] = T^{-1}$ , $[r] = L$ , $[\rho] = ML^{-3}$ , $[s] = MT^{-2}$ .
$M: b + c = 0$ ; $L: a - 3b = 0$ ; $T: -2c = -1$ .
$c = \frac{1}{2},\ b = -\frac{1}{2},\ a = -\frac{3}{2}$ .
So the answer is (b) $\left(-\frac{3}{2}, -\frac{1}{2}, \frac{1}{2}\right)$ .

Report a mistake

Molecular Theory & Factors question from JEE Main 2023 (24 Jan, Shift 2)

More questions on Molecular Theory & Factors