In the experiment for measurement of viscosity $$'\eta'$$ of 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. Choose the correct answer from the options given below:

We analyze each statement about the experiment measuring viscosity $$\eta$$ using a falling ball in a liquid.

Statement A: Graph between terminal velocity V and R is a parabola.

The terminal velocity formula from Stokes' law is: $$V_t = \frac{2R^2(\rho_s - \rho_l)g}{9\eta}$$

Since $$V_t \propto R^2$$, the graph of $$V_t$$ vs $$R$$ is indeed a parabola. Statement A is CORRECT.

Statement B: Terminal velocities of different diameter balls are constant for a given liquid.

Since $$V_t \propto R^2$$, different diameter balls have different terminal velocities. Statement B is INCORRECT.

Statement C: Measurement of terminal velocity depends on temperature.

Viscosity $$\eta$$ is temperature-dependent. As temperature changes, the terminal velocity changes. Statement C is CORRECT.

Statement D: This experiment can assess the density of a given liquid.

From the terminal velocity equation $$V_t = \frac{2R^2(\rho_s - \rho_l)g}{9\eta}$$, if we know $$V_t$$, $$R$$, $$\rho_s$$, and $$\eta$$, we can determine $$\rho_l$$. Statement D is CORRECT.

Statement E: If balls are dropped with some initial speed, the value of $$\eta$$ will change.

Viscosity is an intrinsic property of the liquid. Regardless of the initial speed of the ball, it will eventually reach the same terminal velocity. The measured $$\eta$$ remains unchanged. Statement E is INCORRECT.

The correct statements are A, C, and D. The answer is Option C) A, C and D Only.