JEE Physics 2025 Question with Solution

Given: The experiment measures viscosity $\eta$ of a liquid using a ball of radius $R$ and terminal velocity $V$.

Find: Which statements among A to E are correct.

Using Stokes' law, the terminal velocity is

$$V = \frac{2}{9}\frac{(\rho_s-\rho_l)gR^2}{\eta}$$

So, $V \propto R^2$.

• A: Since $V$ is proportional to $R^2$, the graph of $V$ versus $R$ is a parabola. So A is correct.
• B: Terminal velocity depends on the radius or diameter of the ball, so different diameter balls will not have the same terminal velocity. So B is incorrect.
• C: Viscosity depends on temperature, and hence terminal velocity also depends on temperature. So C is correct.
• D: If the density of the sphere, radius, viscosity, and terminal velocity are known, the density of the liquid can be obtained from the same relation. So D is correct.
• E: Viscosity is a property of the liquid and does not change if the ball is given some initial speed. The ball eventually reaches terminal velocity. So E is incorrect.

Therefore, the correct statements are A, C and D only.

The solution concludes A, C and D only, which corresponds to option D in the given options, even though the answer key marks option B.

Given:

$$V = \frac{2}{9}\frac{(\rho_s-\rho_l)gR^2}{\eta}$$

where $\rho_s$ is the density of the sphere and $\rho_l$ is the density of the liquid.

Find: Evaluate each statement separately.

From the equation, terminal velocity varies as $R^2$, so the $V$ versus $R$ graph is parabolic. Thus A is true.

Because $V$ depends on $R^2$, changing the diameter changes the terminal velocity. Thus B is false.

Since viscosity $\eta$ changes with temperature, the measured terminal velocity also changes with temperature. Thus C is true.

Rearranging the formula,

$$\rho_l = \rho_s - \frac{9\eta V}{2gR^2}$$

so the density of the liquid can be assessed if other quantities are known. Thus D is true.

Giving an initial speed does not alter the liquid property $\eta$. It only affects the initial motion before terminal velocity is reached. Thus E is false.

Hence the correct set is A, C and D only, so the correct option is D.