JEE Main 2026 — Jan 22, Shift 2 — Physics solution

JEE Main2026Jan 22, Shift 2Physics

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height $h$ . If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by ____ %.

A
$- 1$
B
$+ 3$
C
$- 3$
D
$+ 1$

Solution

The capillary rise: $h = \frac{2 T cos θ}{ρ g r}$ .

Taking logarithmic differentials: $\frac{Δ h}{h} = \frac{Δ T}{T} - \frac{Δ ρ}{ρ} - \frac{Δ r}{r}$ .

Given each of $T, ρ, r$ decreases by 1% ( $Δ T / T = Δ ρ / ρ = Δ r / r = - 1%$ ):

$\frac{Δ h}{h} % = (- 1) - (- 1) - (- 1) = + 1%$ .

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