JEE Main · Physics ↓ Falling

Mechanical Properties of Fluids appeared 31 times across 3 years — 3.6% of Physics. This question is from Viscosity and Terminal Velocity.

Year 2026 2025 2024 Total
Questions 9 14 8 31
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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:

Solution & Explanation

Related Formula
VT = (2)/(9) R² gη (d - ρ)
Core Logic

Let us check each statement sequentially:

Statement A: Since VT ∝ R², the graph between terminal velocity V and radius R is a quadratic curve, i.e., a parabola. (True)

Statement B: Different diameters imply different radii, hence terminal velocity will change. It is not constant. (False)

Statement C: Viscosity of a liquid is heavily temperature-dependent, hence VT changes with temperature. (True)

Statement D: Knowing the parameters allows calculation of liquid density ρ. (True)

Statement E: η is a material property of the fluid and does not change based on the initial dropping speed of the ball. (False)

Step 1: Final Conclusion

Statements A, C, and D are correct, which matches option (2).

Pattern Recognition

Terminal velocity problems rely entirely on parsing the proportional relations hidden in Stokes' Law formulation. Note that viscosity coefficient is an intrinsic characteristic parameter independent of kinematics.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Reference Study Guides

Mechanical Properties Of Fluids

More Mechanical Properties of Fluids Previous-Year Questions — Page 7

Q jee_main_2024_31_jan_morning Viscosity And Terminal Velocity
A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?
  • A.
  • B.
  • C.
  • D.

Solution

Related Formula
mg - FB - Fv = ma Fv = 6πη r v
Core Logic

Viscosity And Terminal Velocity diagram for Q46 - JEE Main 2024 Morning
Viscosity And Terminal Velocity diagram for Q46 - JEE Main 2024 Morning

When dropped, three forces act on the ball: Gravity downwards, Buoyant force upwards, and Viscous drag upwards.

mg - FB - Fv = m (dv)/(dt) (ρ (4)/(3)π r³)g - (ρL (4)/(3)π r³)g - 6πη rv = m (dv)/(dt)

Let (4π r³ g(ρ - ρL))/(3m) = K₁ and (6πη r)/(m) = K₂.

(dv)/(dt) = K₁ - K₂ v

Integrating from t=0, v=0:

∫₀^v (dv)/(K₁ - K₂ v) = ∫₀^t dt -(1)/(K₂) ln ((K₁ - K₂ v)/(K₁)) = t v = (K₁)/(K₂) ( 1 - e-K₂ t )

This is an exponential curve starting from the origin and asymptotically approaching the terminal velocity VT = K₁ / K₂.

Chapter Mix

Class 11 Physics: Mechanical Properties Of Fluids

More Mechanical Properties of Fluids Questions — jee_main_2025_28_jan_morning

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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)