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JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Fluid Mechanics

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In the experiment for measurement of viscosity '' 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 will change.
Choose the correct answer from the options given below:
  1. (A)B, D and E only
  2. (B)A, C and D only✓ Correct
  3. (C)C, D and E only
  4. (D)A, B and E only

Answer: (B)

Solution

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


A. Since , the graph of against is a parabola — true.

B. Terminal velocity scales with , so balls of different diameters do not share the same terminal velocity — false.

C. The coefficient of viscosity is strongly temperature-dependent, so any measurement of terminal velocity is affected by temperature — true.

D. Rearranging the terminal velocity formula for shows this experiment can indeed be used to determine the liquid's density, given the other quantities — true.

E. Terminal velocity is the steady-state speed set by the balance of weight, buoyancy and viscous drag; is a property of the liquid alone and does not depend on how the ball was released — false.

So statements A, C and D are correct.

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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