A spherical body of radius r and density falls freely through a viscous liquid having density and viscosity and attains a terminal velocity . Estimated maximum error in the quantity is: (Ignore errors associated with gravitational a

Question

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 $σ, ρ a n d g,$ gravitational acceleration) [2026]

Smart Achievers · Accepted Answer

(4)

$V_{0} = \frac{2 r^{2} g}{9 n} (ρ_{B} - ρ_{L})$

$n = \frac{2 r^{2} g}{9 V_{0}} (ρ_{B} - ρ_{L})$

$\frac{Δ n}{n} = \frac{2 Δ r}{r} + \frac{Δ V_{0}}{V_{0}}$

Solution

Q.
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 $σ, ρ a n d g,$ gravitational acceleration) [2026]

1 $2 [[\frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}]]$

2 $2 [[\frac{Δ r}{r} + \frac{Δ v_{0}}{v_{0}}]]$

3 $2 \frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}$

4 $\frac{2 Δ r}{r} + \frac{Δ v_{0}}{v_{0}}$

Ans.
(4)

$V_{0} = \frac{2 r^{2} g}{9 n} (ρ_{B} - ρ_{L})$

$n = \frac{2 r^{2} g}{9 V_{0}} (ρ_{B} - ρ_{L})$

$\frac{Δ n}{n} = \frac{2 Δ r}{r} + \frac{Δ V_{0}}{V_{0}}$

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Solution

Q. 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 v0. Estimated maximum error in the quantity η is: (Ignore errors associated with σ, ρ and g,gravitational acceleration) [2026]

1 2[Δrr-Δv0v0]

2 2[Δrr+Δv0v0]

3 2Δrr-Δv0v0

4 2Δrr+Δv0v0