Errors in measurementMedium
Question
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)
Options
A.$2\frac{\Delta r}{r} - \frac{\Delta v_{0}}{v_{0}}$
B.$\frac{2\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}}$
C.$2\left\lbrack \frac{\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}} \right\rbrack$
D.$2\left\lbrack \frac{\Delta r}{r} - \frac{\Delta v_{0}}{v_{0}} \right\rbrack$
Solution
$v_{0} = \frac{2}{9}\frac{r^{2}\text{ }g}{n}\left( \rho_{B} - \rho_{L} \right)$
$${n = \frac{2}{9}\frac{r^{2}\text{ }g}{v_{0}}\left( \rho_{B} - \rho_{L} \right) }{\frac{\Delta n}{n} = \frac{2\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}}}$$
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