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Viscosity and Newton's Law of Viscous Force

NEET > Physics > Properties of Bulk Matter > Fluid Mechanics > Viscosity and Newton's Law of Viscous Force

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NEET Physics - Fluid Mechanics

Viscosity and Newton's Law of Viscous Force โ€“ Complete Notes, Revision, Important Questions & Downloads

Viscosity and Newton's Law of Viscous Force in NEET Physics is built around three linked subtopics: Definition of Viscosity, Newton's Law of Viscous Force, and Temperature and Pressure Effects on Viscosity. The exam usually tests whether you can convert the idea of internal friction into the force law F = -eta A(dv/dx), identify the sign and unit of eta, and read what happens when the layer gap or relative speed changes. A standard numerical gives two plates separated by a thin liquid film and asks for force, coefficient of viscosity, or the missing gap. The same coefficient then reappears in Poiseuille flow and terminal-velocity problems, so this topic is small in theory but active in application.

โฌ‡ Download Notes PDFView Important Questions โ†’
8 SubtopicsShear-Force LawFormula + Numerical
Expected QuestionsQ
0-1
Direct questions are irregular, but viscosity language and eta-based substitutions show up inside Stokes-law and capillary-flow numericals.
Time Requiredโฑ
2-3 hours
About one short theory pass, one formula drill, and one focused numerical set on plate motion, velocity gradient, and temperature trend.
Difficultyโšก
Medium
The formula is short; marks are lost when students confuse dv/dx with v/x, miss unit conversion between poise and SI, or reverse the liquid-gas temperature trend.
NRI USA Curriculum GapUS
Medium
Many US-track students see drag qualitatively, but NEET expects fast plate-shear calculations, CGS-SI conversion, and a direct comparison of liquid versus gas viscosity with temperature.
8Subtopics
8Practice Questions
4Free Downloads
2-3 hrsPrep Time
โฌ‡ Get Free Downloads

NEET Weightage - Viscosity and Newton's Law of Viscous Force

Fluid Mechanics (Chapter 11)
NEET YearQuestions from this TopicBarMarks
20240
ย 
0 Q
0
20230
ย 
0 Q
0
20220
ย 
0 Q
0
20211
ย 
1 Q
4
20200
ย 
0 Q
0
20190
ย 
0 Q
0
6-Year Snapshot (2019-2024)1ย 4
The safest direct test is the plate-shear form F = eta A(dv/dx), where NEET may hide dv/dx inside mixed units such as cm/s and mm.
Temperature behaviour is a common trap: viscosity decreases for liquids when temperature rises, but increases for gases because molecular collisions become more frequent.

Even when the question is framed around terminal velocity or Poiseuille flow, the coefficient eta from Newton's law remains the controlling material parameter.
๐Ÿ“Š
0.2
Avg Questions / Year
๐ŸŽฏ
4
Total Marks (6 yrs)
๐Ÿ“ˆ
Irregular
Pattern
โš ๏ธ
Medium
Difficulty

Exam Strategy for Viscosity Questions

1

Lock the force law before solving anything Memorise F = -eta A(dv/dx) and eta = F / [A(dv/dx)]. Before substituting, check whether the question gives a velocity difference, a separation, or both. The trap is using v/x without first converting the gap into SI units. Recognise this topic whenever two adjacent layers or two plates move with different speeds.

2

Treat velocity gradient as a rate, not a speed Memorise that dv/dx is change of velocity per perpendicular distance between layers. Check whether the distance is in mm, cm, or m. The trap is inserting only the speed of the moving layer and ignoring the lower layer speed. This topic is present whenever the problem mentions 'relative motion of layers' or 'thin liquid film'.

3

Keep units of viscosity ready in both systems Memorise SI unit N s m^-2 or Pa s, CGS unit dyne s cm^-2 or poise, and dimension [M L^-1 T^-1]. Check the unit system before comparing values. The trap is treating poise and poiseuille as the same numerical unit; 1 poiseuille = 10 poise. Spot this topic when answer choices differ only by powers of ten.

4

Separate liquid and gas temperature trends explicitly Memorise: liquid viscosity decreases with temperature, gas viscosity increases with temperature. Check whether the medium named is oil, water, glycerin, or air before choosing the trend. The trap is carrying the liquid rule over to gases. This topic shows up whenever the question heats a fluid and asks about flow ease or internal resistance.

Download Study Notes - Viscosity and Newton's Law of Viscous Force

PDF ยท Cheat Sheet ยท MCQ Set ยท PYQ
๐Ÿ“˜
Full Notes
Topic notes covering all three subtopics: definition of viscosity, the complete Newton law relation with sign, area, and velocity gradient, and the temperature-pressure trend used in NEET fluid-mechanics questions.
8 subtopicsWorked plate examplesUnit table
Download PDF
๐Ÿ“—
Formula Sheet
One quick sheet with F = -eta A(dv/dx), eta unit conversion, dimension [M L^-1 T^-1], and one worked example each for velocity gradient and temperature-effect recall.
1 pageAll key formulas
Download PDF
๐Ÿ“™
MCQ Practice
Practice set focused on layer-separation numericals, force comparisons after doubling area or speed gradient, and the liquid-versus-gas temperature rule.
Application MCQsDetailed solutions
Download PDF
๐Ÿ“•
PYQ
Previous-year revision tracker for viscosity-linked NEET questions, especially direct eta questions and viscosity terms hidden inside terminal-velocity or capillary-flow problems.
Year taggedQuick recap
Download PDF

Subtopics in Viscosity and Newton's Law of Viscous Force

2-Column Table
Column AColumn B
Definition of Viscosityโ†—
Newton's Law of Viscous Forceโ†—
Temperature and Pressure Effects on Viscosityโ†—
Effective liquid resistance in parallel combinationโ†—
Increase in all directionsโ†—
Never increasesโ†—
Bar and millibarโ†—
The force between atoms and moleculesโ†—

Rapid Revision - Viscosity and Newton's Law of Viscous Force

Concept โ†’ Trap โ†’ Example

1) Definition of Viscosity

Meaning + Gradient

Viscosity is the property of a fluid due to which it opposes relative motion between its different layers; the relevant rate is the velocity gradient dv/dx.

  • Use the word 'relative' carefully: if both layers move, take the velocity difference, not just the speed of one layer.
  • High viscosity means stronger resistance to shear flow, so honey and glycerin oppose layer sliding more than water or air.
  • Common NEET trap: treating viscosity as resistance against the whole fluid bulk instead of resistance between adjacent layers.
Example (NEET-style)If the top layer moves at 0.40 m/s and a layer 2 mm below moves at 0.10 m/s, then dv/dx = (0.40 - 0.10) / 0.002 = 150 s^-1. That gradient, not the speed 0.40 m/s alone, enters the force law.

2) Newton's Law of Viscous Force

Force Law + Units

Newton's law of viscous force is F = -eta A(dv/dx); hence eta = F / [A(dv/dx)], with SI unit N s m^-2 and dimension [M L^-1 T^-1].

  • Force is directly proportional to contact area A, so doubling plate area doubles the viscous force if eta and dv/dx stay fixed.
  • The minus sign shows opposition to relative motion; it tells direction, not a negative magnitude of viscosity.
  • Common NEET trap: mixing poise and poiseuille or forgetting that 1 poiseuille = 10 poise while converting answer choices.
Example (NEET-style)For eta = 0.01 Pa s, area A = 0.20 m^2, and dv/dx = 50 s^-1, the magnitude of force is F = eta A(dv/dx) = 0.01 x 0.20 x 50 = 0.10 N. If the plate gap is halved while speed difference stays same, dv/dx doubles and the force becomes 0.20 N.

3) Temperature and Pressure Effects on Viscosity

Trend + Physical Cause

With increase in temperature, the coefficient of viscosity of liquids decreases but that of gases increases; the textbook also lists Andrade's empirical relation for temperature dependence.

  • For liquids, heating weakens effective cohesive hold between neighboring layers, so they slide more easily and viscosity falls.
  • For gases, heating increases random molecular motion and collision activity, so momentum transfer between layers rises and viscosity increases.
  • Common NEET trap: applying the liquid trend to air or any gas because the words 'heated fluid flows faster' sound similar.
Example (NEET-style)A research table commonly quotes water near 20 C at about 1.0 mPa s and near 100 C at about 0.3 mPa s, showing the liquid trend clearly. Air moves the other way: its viscosity rises slightly when temperature increases, so hot air is not treated like hot oil in this question type.

US Curriculum Gaps - Viscosity and Newton's Law of Viscous Force

NRI students coming from common US high-school sequences usually need two targeted repairs before this topic feels automatic in NEET.

AP Physics 1: fluids coverage is broader than NEET shear-law drilling

AP Physics 1 usually emphasises pressure, buoyancy, and continuity, but does not repeatedly train the plate-shear numerical F = eta A(dv/dx) with mixed-unit velocity gradients. A NEET student must be able to move from wording to formula in one line.

  • Expect direct substitution problems with area, speed difference, and plate separation given in different unit systems.
  • Memorise eta as dynamic viscosity, not just a vague flow-resistance idea.
  • Practise converting mm to m and poise to SI before solving the algebra.

AP Physics C: Mechanics: viscosity is usually outside the core mechanics set

Students strong in calculus-based mechanics may still miss this NEET topic because AP Physics C: Mechanics does not make dynamic viscosity, poise, or layer-by-layer internal friction a routine assessed skill. NEET expects recall of the trend for liquids and gases without derivation time.

  • Build a one-glance memory pair: liquid up in temperature means viscosity down; gas up in temperature means viscosity up.
  • Link eta to later topics such as terminal velocity and Poiseuille flow so the symbol is not memorised in isolation.
  • Treat the sign in F = -eta A(dv/dx) as a direction cue that opposes motion, not as a separate negative-valued constant.

NEET-style practice questions - Viscosity and Newton's Law of Viscous Force

4 application MCQs
1A square plate of side 0.10 m moves at 0.10 m/s over a fixed plate with a water film of thickness 5 x 10^-4 m between them. If eta = 0.01 Pa s, what force is needed to maintain uniform motion?Newton's law of viscous force
1 x 10^-2 N
2 x 10^-2 N
5 x 10^-4 N
5 x 10^-2 N
Use F = eta A(dv/dx). The plate area is A = (0.10)^2 = 0.01 m^2. The lower plate is fixed, so dv = 0.10 m/s and dx = 5 x 10^-4 m, giving dv/dx = 200 s^-1. Hence F = 0.01 x 0.01 x 200 = 0.02 N. Option 2 is correct. Option 1 appears if the area is taken wrongly as 0.001 m^2. Option 3 comes from multiplying by dx instead of dividing by it. Option 4 is an overestimate from missing the square on plate side.
2Two adjacent liquid layers have speeds 26 cm/s and 14 cm/s and are separated by 0.20 mm. The velocity gradient is:Definition of viscosity
60 s^-1
600 s^-1
6 s^-1
6000 s^-1
Relative speed is 26 - 14 = 12 cm/s = 0.12 m/s. Separation is 0.20 mm = 2 x 10^-4 m. Therefore dv/dx = 0.12 / (2 x 10^-4) = 600 s^-1. Option 2 is correct. Option 1 comes from failing to convert cm/s to m/s or mm to m consistently. Option 3 is a decimal-shift error. Option 4 results from converting 0.20 mm wrongly as 2 x 10^-5 m. The question tests whether you interpret velocity gradient as change in velocity per perpendicular distance.
3Engine oil and air are both heated. Which option matches the expected change in their viscosities?Temperature and Pressure Effects on Viscosity
Oil increases, air decreases
Oil decreases, air increases
Both decrease
Both increase
For liquids such as engine oil, higher temperature reduces cohesive hold between neighboring layers, so viscosity decreases. For gases such as air, higher temperature increases random motion and momentum transfer between layers, so viscosity increases. Therefore option 2 is correct. Option 1 is exactly the reversal NEET uses as a trap. Options 3 and 4 ignore that liquid and gas viscosity respond oppositely to heating. The key is to classify the medium first, then apply the correct trend.
4A liquid layer problem gives eta = 5 poise. What is the SI value of eta?Coefficient of viscosity
0.05 Pa s
0.5 Pa s
5 Pa s
50 Pa s
The CGS unit poise and the SI unit poiseuille are related by 1 poiseuille = 10 poise, so 1 poise = 0.1 Pa s. Therefore 5 poise = 5 x 0.1 = 0.5 Pa s, which is option 2. Option 1 corresponds to multiplying by 0.01 instead of 0.1. Option 3 treats poise as numerically equal to Pa s, and option 4 over-multiplies by a factor of 10. This is a standard unit-conversion trap around viscosity.

Practice Problems - Viscosity and Newton's Law of Viscous Force

Click "Reveal Answer" after attempting
1A liquid film 1.0 mm thick separates two large plates of area 0.20 m^2. The upper plate moves at 0.30 m/s while the lower plate is at rest. If eta = 0.015 Pa s, what tangential force is required?
0.45 N
0.90 N
0.30 N
0.15 N
๐Ÿ‘ Reveal Answer
Correct option: 2. Use F = eta A(dv/dx). Here A = 0.20 m^2, dv = 0.30 m/s, dx = 1.0 mm = 1.0 x 10^-3 m. So dv/dx = 300 s^-1. Therefore F = 0.015 x 0.20 x 300 = 0.90 N. Option 1 would come from forgetting the factor 2 in area scaling, option 3 from using dx as 3 x 10^-3 m, and option 4 from a direct arithmetic slip.
2The viscous force between two layers is 0.08 N on an area of 0.10 m^2. If the velocity changes by 0.40 m/s over 2.0 mm, find eta.
0.002 Pa s
0.004 Pa s
0.008 Pa s
0.016 Pa s
๐Ÿ‘ Reveal Answer
Correct option: 2. Rearranging Newton's law, eta = F / [A(dv/dx)]. The gradient is dv/dx = 0.40 / (2.0 x 10^-3) = 200 s^-1. Then eta = 0.08 / (0.10 x 200) = 0.08 / 20 = 0.004 Pa s. Option 1 results from taking 2 mm as 2 x 10^-2 m, option 3 from missing the division by area, and option 4 from doubling instead of halving the denominator.
3A liquid at 20 C has viscosity eta. It is heated so that the cohesive hold between layers weakens. Which statement best matches the expected result for the same geometry and same velocity gradient?
Viscous force increases because hotter fluids always resist more
Viscous force remains same because area is unchanged
Viscous force decreases because eta decreases for liquids
Viscous force becomes zero because internal friction vanishes
๐Ÿ‘ Reveal Answer
Correct option: 3. For liquids, increasing temperature decreases viscosity. Since F = eta A(dv/dx), if area and velocity gradient remain unchanged, the force must decrease in the same ratio as eta. Option 1 incorrectly imports the gas trend into a liquid. Option 2 ignores that viscosity itself changes. Option 4 is physically impossible because heating lowers internal resistance but does not eliminate it.
4A plate problem is solved once with gap x and then again with gap x/2, while eta, area, and relative speed are unchanged. How does the viscous force change?
It becomes half
It becomes double
It becomes four times
It is unchanged
๐Ÿ‘ Reveal Answer
Correct option: 2. Since F = eta A(dv/dx) and dv/dx = dv/x, halving the gap doubles the gradient. Therefore the viscous force also doubles. Option 1 reverses the proportionality, option 3 would require the gap to reduce by a factor of four, and option 4 ignores the role of x in the velocity gradient. This is one of the quickest proportionality checks in viscosity numericals.

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Frequently Asked Questions - Viscosity and Newton's Law of Viscous Force

Notes ยท Downloads ยท Revision ยท Important Questions
Why is viscosity described as internal friction and not ordinary surface friction?
Because the resisting force arises between adjacent layers of the same fluid when they try to move with different velocities. In ordinary surface friction, two solid surfaces interact at their boundary. In viscosity, the fluid still transmits a tangential opposing force, but the mechanism is layer-to-layer momentum transfer inside the fluid itself. That is why velocity gradient, not just contact alone, is the key variable in Newton's law of viscous force.
What exactly does dv/dx mean in a viscosity problem?
dv/dx is the rate at which velocity changes per unit perpendicular distance between neighboring layers. If one layer moves at 0.50 m/s and another 1 mm away moves at 0.20 m/s, the relevant change is 0.30 m/s across 0.001 m, not simply 0.50 divided by 0.001. Many wrong answers come from using one speed instead of the speed difference or from forgetting to convert mm to m before calculating the gradient.
Why does the force formula carry a negative sign?
The negative sign in F = -eta A(dv/dx) indicates direction: viscous force opposes the relative motion responsible for the shear. It does not mean viscosity is negative. If the upper layer tends to move faster, the viscous force on it acts backward and the force on the slower neighboring layer acts forward. In numerical NEET questions, you usually use the magnitude eta A(dv/dx) unless vector direction is explicitly asked.
How do I remember the unit and dimension of coefficient of viscosity?
Start from eta = F / [A(dv/dx)]. Force contributes N, area contributes m^2 in the denominator, and dv/dx contributes s^-1. So eta has SI unit N s m^-2, which is also Pa s. In CGS, the unit is dyne s cm^-2 or poise. The dimension becomes [M L^-1 T^-1]. Deriving it once from the formula is better than memorising an isolated symbol string.
Why does liquid viscosity decrease with temperature while gas viscosity increases?
In liquids, neighboring molecules are already close, so stronger heating mainly weakens cohesive hold and lets layers slide more easily; viscosity therefore falls. In gases, molecules are far apart, so the important effect of heating is more vigorous random motion and more momentum transfer between layers; viscosity therefore rises. NEET often tests this as a contrast question where the student must classify the medium first and only then apply the temperature rule.
Does pressure have the same importance as temperature in standard NEET viscosity questions?
Not usually. Within standard Class 11 and NEET-style treatment, temperature trend is the more visible and frequently tested rule. Pressure dependence exists, but it is much smaller for liquids under ordinary conditions and is not usually the main discriminating idea unless the question explicitly pushes you toward high-pressure or gas-behavior reasoning. If a problem only mentions heating oil or heating air, temperature is the intended trigger, not pressure.
Where else in fluid mechanics does this coefficient eta reappear?
The same coefficient of viscosity controls Stokes drag, terminal velocity in a viscous medium, and Poiseuille's expression for capillary flow. That is why this topic matters even when its own direct question count is low. Once you know what eta means physically, later formulas stop looking disconnected: they all measure how strongly a fluid resists relative motion or momentum transfer under flow.
What is the fastest way to avoid mistakes in plate-shear numericals?
Write four symbols in order before touching the calculator: A, dv, dx, eta. Convert every length to metre, then form dv/dx, and only then multiply by eta A. This sequence prevents the most common errors: using velocity instead of velocity difference, leaving the gap in mm, and forgetting that force is inversely proportional to plate separation. If answer choices differ by factors of 10, unit conversion is usually the actual test point.
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Definition of Viscosity

Newton's Law of Viscous Force

Temperature and Pressure Effects on Viscosity

Effective liquid resistance in parallel combination

Increase in all directions

Never increases

Bar and millibar

The force between atoms and molecules

Subtopics

Definition of Viscosity

Newton's Law of Viscous Force

Temperature and Pressure Effects on Viscosity

Effective liquid resistance in parallel combination

Increase in all directions

Never increases

Bar and millibar

The force between atoms and molecules

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Viscosity and Newton's Law of Viscous Force > The force between atoms and molecules > The force between atoms and molecules
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Definition of Viscosity

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