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

2 [frac Δ r r +frac Δ v 0 v 0 ]

2 [frac Δ r r -frac Δ v 0 v 0 ]

Physics · Mechanical Properties of Matter

JEE Main 2026 — 21 January, Evening Shift — Question 36

A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $\mathrm{v}_{0}$ . Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma, \rho$ and g , gravitational acceleration)

Option A:
$2 \frac{\Delta r}{r}-\frac{\Delta v_{0}}{v_{0}}$
Option B:
$\frac{2 \Delta r}{r}+\frac{\Delta v_{0}}{v_{0}}$
Correct
Option C:
$2\left[\frac{\Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \mathrm{v}_{0}}{\mathrm{v}_{0}}\right]$
Option D:
$2\left[\frac{\Delta \mathrm{r}}{\mathrm{r}}-\frac{\Delta \mathrm{v}_{0}}{\mathrm{v}_{0}}\right]$

Answer: B

Step-by-step solution

$\mathrm{v}_{0}=\frac{2}{9} \frac{\mathrm{r}^{2} \mathrm{~g}}{\mathrm{n}}\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right)$ $\mathrm{n}=\frac{2}{9} \frac{\mathrm{r}^{2} \mathrm{~g}}{\mathrm{v}_{0}}\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right)$ $\frac{\Delta \mathrm{n}}{\mathrm{n}}=\frac{2 \Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \mathrm{v}_{0}}{\mathrm{v}_{0}}$

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Exam: JEE Main 2026
Paper: 21 January, Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Viscosity

Answer: B

Step-by-step solution

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