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 v_0. Estimated maximum error in the quantity eta is : (Ignore errors associated with sigma, rho and g , gravitational acceleration)

v_0=(2 / 9) frac r^2 g n(rho_ B-rho_ L) n=(2 / 9) frac r^2 g v_0(rho_ B-rho_ L) fracDelta n n=frac2 Delta r r+fracDelta v_0 v_0

A spherical body of radius r and density sigma falls fr... | null (Physics)

JEE Mains 2026 21st January Shift 2

Physics

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)

2 \frac{\Delta r}{r}-\frac{\Delta v_{0}}{v_{0}}

\frac{2 \Delta r}{r}+\frac{\Delta v_{0}}{v_{0}}

2\left[\frac{\Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \mathrm{v}_{0}}{\mathrm{v}_{0}}\right]

2\left[\frac{\Delta \mathrm{r}}{\mathrm{r}}-\frac{\Delta \mathrm{v}_{0}}{\mathrm{v}_{0}}\right]

Correct Answer:

\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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