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KCET · Physics · Mechanical Properties of Fluids

While determining the coefficient of viscosity of the given liquid, a spherical steel ball sinks by a distance \(\mathrm{h}=0.9 \mathrm{~m}\). The radius of the ball \(\mathrm{r}=\sqrt{3} \times 10^{-3} \mathrm{~m}\). The time taken by the ball to sink in three trails are tabulated as follows.
Trial No.Time taken by the ball to fall by h (in second)
1.2.75
2.2.65
3.2.70
The difference between the densities of the steel ball and the liquid is \(7000 \mathrm{~kg} \mathrm{~m}^{-3}\). If \(\mathrm{g}=10 \mathrm{~ms}^{-2}\), then the coefficient of viscosity of the given liquid at room temperature is

  1. A \(0.14 \mathrm{~Pa} . \mathrm{s}\)
  2. B \(0.14 \times 10^{-3} \mathrm{~Pa} . \mathrm{s}\)
  3. C \(14 \mathrm{~Pa} . \mathrm{s}\)
  4. D 0.28 Pa.s
Verified Solution

Answer & Solution

Correct Answer

(A) \(0.14 \mathrm{~Pa} . \mathrm{s}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{t}_{\text {avg}}=\frac{2.75+2.65+2.70}{3}=2.7 \mathrm{sec} \)
\( \text {Terminal velocity }=\frac{\mathrm{h}}{\mathrm{t}_{\text {avg }}} \)
\( \mathrm{V}_{\mathrm{t}}=\frac{1}{3} \mathrm{~m} / \mathrm{s} \)
\( \mathrm{n}=\frac{2}{9} \frac{\pi^2 \mathrm{~g}\left(\mathrm{~S}_{\text {stell }}-\mathrm{S}_{\text {liquid }}\right)}{\mathrm{V}_{\mathrm{t}}} \)
\( \mathrm{n}=0.14 \mathrm{~Pa} . \mathrm{S}\)