Question

In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider 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.

• A. \(B\), \(D\) and \(E\) Only
• B. \(A\), \(C\) and \(D\) Only
• C. \(A\), \(B\) and \(E\) Only
• D. \(C\), \(D\) and \(E\) Only

Hint:

Understanding the physical principles behind measurements can help clarify which variables influence the results in experimental setups.

Answer 1

The Correct Option is B

Analysis of each statement:

A. Terminal velocity $ V $ is calculated using the formula: $$ V = \frac{2}{9} \frac{r^2 (\rho_s - \rho_l)g}{\eta} $$ Here, $ r $ is the ball's radius, $ \rho_s $ is the ball's density, $ \rho_l $ is the liquid's density, $ g $ is the acceleration due to gravity, and $ \eta $ is the liquid's viscosity. Given that $ V $ is proportional to $ r^2 $ ($ V \propto r^2 $), a plot of terminal velocity $ V $ against $ r $ (or $ R $) will yield a parabolic curve. Statement A is accurate.

B. The terminal velocity is influenced by the ball's radius (or diameter). Balls with different diameters will exhibit varying terminal velocities when submerged in the same liquid. Statement B is inaccurate.

C. Terminal velocity measurements are sensitive to temperature variations. The viscosity of a liquid is temperature-dependent. Typically, as temperature rises, the viscosity of most liquids declines, which in turn affects the terminal velocity. Statement C is accurate.

D. This experimental setup can be employed to determine the density of an unknown liquid. By measuring the terminal velocity of a ball with a known density and radius, and knowing the liquid's viscosity, the liquid's density can be derived from the terminal velocity equation. Statement D is accurate.

E. The viscosity $ \eta $ of the liquid remains constant, irrespective of the initial speed at which balls are dropped. Viscosity is an intrinsic property of the liquid and is not affected by the ball's initial velocity. While the time taken to reach terminal velocity may differ based on whether the ball is thrown or released from rest, this does not alter the liquid's viscosity. Statement E is inaccurate.

Conclusion:
Statements A, C, and D are correct.

Final Answer:
The final answer is $ (2)\ \text{A, C and D only} $.