JEE Main 2026 — Jan 21, Shift 2 — Physics solution

JEE Main2026Jan 21, Shift 2Physics

A spherical body of radius r and density $σ$ falls freely through a viscous liquid having density $ρ$ and viscosity $η$ and attains a terminal velocity $v_{0}$ . Estimated maximum error in the quantity $η$ is : (Ignore errors associated with $σ$ , $ρ$ and g, gravitational acceleration)

A
$2 \frac{Δ r}{r} - \frac{Δ v _{0}}{v _{0}}$
B
$\frac{2Δ r}{r} + \frac{Δ v _{0}}{v _{0}}$
C
$2 [\frac{Δ r}{r} + \frac{Δ v _{0}}{v _{0}}]$
D
$2 [\frac{Δ r}{r} - \frac{Δ v _{0}}{v _{0}}]$

Solution

Stokes terminal velocity gives $v_{0} = \frac{2 r ^{2} g ( σ - ρ )}{9 η}$ , so $η = \frac{2 g ( σ - ρ )}{9} \cdot \frac{r ^{2}}{v _{0}}$ .

Treating $σ, ρ, g$ as exact, the relative error in $η$ comes from $r^{2} / v_{0}$ :

$\frac{Δ η}{η} = 2 \frac{Δ r}{r} + \frac{Δ v _{0}}{v _{0}}$ .

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