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:

<p>We know, terminal velocity of a sphere of radius R in a liquid of viscosity $\eta$,</p> <p>$v = {2 \over 9}{{{R^2}} \over \eta }(\sigma - \rho )$ .... (1)</p> <p>where, $\sigma$ = mass of density of sphere</p> <p>$\rho$ = density of liquid</p> <p>we can see, $v \propto {R^2}$ (for constant $\eta,\sigma$ & $\rho$)</p> <p>Hence, graph between v and R is parabola.</p> <p>As v depends on R so the terminal velocities of different diameter balls will be different.</p><p>We know, the viscosity of a liquid usually decreases as the temperature increases and $v \propto {1 \over \eta }$</p> <p>So terminal velocity depends on the temperature. $T \uparrow \Rightarrow \eta \downarrow \Rightarrow v \uparrow$</p> <p>As the equation $v = {2 \over 9}{{{R^2}} \over v}(\sigma - \rho )$ involves density of liquid $\rho$. So the experiment can be utilized to asses it.</p> <p>From (1), $\eta = {2 \over 9}{{{R^2}} \over v}(\sigma - \rho )$</p> <p>Here, $\eta$ does not depend on initial speed of the sphere. Hence, option 3 is correct.</p>