In the experiment for measurement of viscosity $\eta$ of a given liquid with a ball having radius $R$, consider the following statements:
A. Graph between terminal velocity $V$ and $R$ will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of $\eta$ will change.
Choose the correct answer from the options given below:
Answer: (C) A, C and D only
Terminal velocity $V = \dfrac{2R^2(\rho - \sigma)g}{9\eta}$.
- A: $V \propto R^2$, a parabola: correct.
- B: $V$ depends on $R$, so different balls have different terminal velocities: wrong.
- C: $\eta$ changes with temperature, so $V$ does too: correct.
- D: If $\eta$ is known, measuring $V$ gives $\sigma$, the density of the liquid: correct.
- E: $\eta$ is a property of the liquid; the initial speed only changes how quickly terminal velocity is reached: wrong.
A, C and D only.
Solution by Sreeraj P, M.Sc Physics