#terminal velocity

PHYSICS

What is the reason a liquid’s terminal velocity depends on its radius when falling through a viscous medium?

Stokes’ law ( F = 6 π eta a v ) shows that viscous force is proportional to radius ( a ), while weight ( 4/3 π a³ rho g ) depends on a³ . At terminal velocity, these balance, making v propto a² .

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Laws of Motion, Work Energy Power, Gravitation and System of Particles, Topic: Newton's laws, work-energy theorem and rotational dynamics.

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Equation of Continuity and Flow Rate

Which of the following statements is correct about terminal velocity?

Terminal velocity occurs when the viscous force (proportional to velocity) equals the net gravitational force, resulting in zero acceleration and constant speed, as per Stokes’ law. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It occurs when forces balance. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Fluid Pressure, Pascal's Law and Manometers

What is the primary reason a heavy object falls faster than a lighter one through a viscous fluid?

Terminal velocity (v∝(mg−Fb)/6πηa) depends on weight minus buoyant force. A heavier object has a greater net downward force, increasing its terminal velocity compared to a lighter object of the same size.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Viscosity, Stokes' Law and Reynolds Number

A sphere of radius 0.02m falls through glycerine (η\=0.83Pa s) at a terminal velocity of 0.1m/s. What is the viscous dra

Using Stokes’ law: F = 6πηav. η = 0.83Pa s, a = 0.02m, v = 0.1m/s. F = 6×3.14×0.83×0.02×0.1≈0.0313N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.031 N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Bernoulli's Theorem and Applications

What is the reason a liquid’s terminal velocity depends on its radius when falling through a viscous medium?

Stokes’ law (F = 6πηav) shows that viscous force is proportional to radius (a), while weight (43πa3ρg) depends on a3. At terminal velocity, these balance, making v∝a2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Viscous force depends on radius. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Universal Law of Gravitation

What happens to an object falling through a viscous fluid when the viscous force equals the gravitational force?

When the viscous force (from Stokes’ law) plus buoyant force equals the gravitational force, the net force becomes zero, and the object reaches terminal velocity, moving at a constant speed, as explained in the chapter.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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