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

Let's analyze each statement:

A. The terminal velocity $ V $ is given by:
$$ V = \frac{2}{9} \frac{r^2 (\rho_s - \rho_l)g}{\eta} $$
where $ r $ is the radius of the ball, $ \rho_s $ is the density of the ball, $ \rho_l $ is the density of the liquid, $ g $ is the acceleration due to gravity, and $ \eta $ is the viscosity of the liquid.
Since $ V \propto r^2 $, the graph between terminal velocity $ V $ and $ r $ (or $ R $) will be a parabola.
So, statement A is correct.

B. The terminal velocity depends on the radius (or diameter) of the ball. Different diameter balls will have different terminal velocities for a given liquid.
So, statement B is incorrect.

C. Measurement of terminal velocity is dependent on the temperature. The viscosity of the liquid is temperature-dependent. As temperature increases, the viscosity of most liquids decreases, affecting the terminal velocity.
So, statement C is correct.

D. This experiment can be utilized to assess the density of a given liquid. By measuring the terminal velocity of a ball with known density and radius, and knowing the viscosity, we can solve for the density of the liquid in the equation for terminal velocity.
So, statement D is correct.

E. If balls are dropped with some initial speed, the value of $ \eta $ will not change. The viscosity is a property of the liquid and does not depend on the initial speed of the ball. Although the ball takes a longer/shorter amount of time depending on whether it is thrown or released, this does not affect the viscosity.
So, statement E is incorrect.

Conclusion:
The correct statements are A, C, and D.

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