JEE Main 2025 Jan 28 Shift 1, Physics Q2: Properties of Fluids

JEE Main2025Jan 28, Shift 1Physics

In the experiment for measurement of viscosity ' $η$ ' 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 $η$ will change.

Choose the correct answer from the options given below:

A
B, D and E only
B
A, C and D only
C
C, D and E only
D
A, B and E only

Solution

The terminal velocity for a sphere falling through a viscous liquid is

$V_{T} = \frac{2}{9} R^{2} \frac{g}{η} (d - ρ)$

where $d$ is the density of the ball, $ρ$ the density of the liquid.

A. $V_{T} \propto R^{2}$ at fixed $η$ , $g$ , $d$ , $ρ$ . The $V_{T}$ vs $R$ plot is a parabola. True.

B. $V_{T}$ scales with $R^{2}$ , so different-diameter balls have different terminal speeds in the same liquid. False.

C. Viscosity $η$ depends strongly on temperature, so $V_{T}$ does too. True.

D. Knowing $V_{T}$ , $R$ , $η$ , $g$ , $d$ lets us solve for $ρ$ from Stokes' law. True.

E. $η$ is a property of the fluid; it does not change with the initial speed of the ball. False.

$∴$ A, C and D only.

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JEE Main 2025 Jan 28 Shift 1, Physics Q2: Properties of Fluids

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