NEET 2026 · Q12 Medium
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✓ Key
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💡 Verified Solution & 30-Second Hack
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Verified Against NTA Final Answer Key
Option (1) : Graph (1): Line starts at sigma / rho = 1 on the horizontal axis and increases linearly
📚 Properties of Bulk Matter Medium
📋 Given Parameters & Problem Setup
Experiment Measurement of viscosity of liquids using terminal velocity
Spherical Balls Identical radius r, varying density sigma
Liquid Density rho (constant)
Variables to Plot Terminal velocity v vs density ratio (sigma / rho)
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⏱️ Bypasses complex algebraic plotting. The 30-Second Exam Hall Shortcut: ⚡ Root Finding & Physical Cutoff Shortcut
Find where terminal velocity equals zero!
1 Recall Stokes' Law terminal velocity: v_t = (2/9) * [r^2 * g / eta] * (sigma - rho).
2 Factor out liquid density rho: v_t = C * [(sigma / rho) - 1], where C = (2/9) * r^2 * g * rho / eta is positive.
3 Set v_t = 0 ==> (sigma / rho) - 1 = 0 ==> sigma / rho = 1.
4 Therefore, the graph MUST intersect the horizontal axis at exactly sigma / rho = 1.
5 For sigma / rho < 1, the sphere is less dense than the liquid, so buoyant force exceeds gravity; the ball floats and cannot fall downward.
6 Hence, v = 0 for sigma/rho <= 1, and increases linearly with slope C for sigma/rho > 1.
7 Look at the graphs: Only Graph (1) starts directly at (1, 0) on the axis. Solved in 15 seconds!
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Why You Can 100% Trust This Shortcut: Terminal velocity represents steady-state descent where Weight = Buoyant Force + Viscous Drag. At sigma = rho, Weight = Buoyancy, so net sinking force is zero and v_t = 0.
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Step-by-Step Rigorous Workflow & Mathematical Proof
Step 1
Formulate Dynamic Equilibrium for a Falling Sphere
When a sphere reaches terminal velocity v_t in a viscous medium, net downward acceleration is zero:
- • Weight of sphere: W = sigma * V * g = sigma * (4/3 pi r^3) * g.
- • Upthrust (Buoyant force): F_B = rho * V * g = rho * (4/3 pi r^3) * g.
- • Stokes' viscous drag force: F_v = 6 pi eta r v_t.
Step 2
Express Terminal Velocity in terms of Density Ratio
Equate net gravitational force to viscous drag and solve for v_t:
- • Let x = sigma / rho and constant k = (2 r^2 g rho) / (9 eta).
- • Then v_t = k * (x - 1).
- • This is a straight line equation of the form y = m(x - x_0) with x-intercept x_0 = 1.
Step 3
Analyze Physical Boundary Conditions and Graph Shape
Evaluate physical behavior across different density regimes:
- • If sigma < rho, the ball floats upward (or remains at rest on the surface); falling terminal velocity is 0.
- • At sigma / rho = 1, downward terminal velocity is exactly 0.
- • For sigma / rho > 1, terminal velocity increases linearly with slope k.
- • Matches Graph (1) perfectly, corresponding to Option (1).
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4-Option Deep Scan
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
1 Option (1)
✓ 100% Correct Verdict & Scientific Reason:
Exact physical representation of Stokes' Law and Archimedes' principle; confirmed by Official NTA Key.
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Why this is airtight: Correctly identifies that terminal descent requires sigma > rho and starts at x = 1.
Note: Flawless experimental physics.
2 Option (2)
✗ Incorrect Verdict & Scientific Reason:
Violates static equilibrium.
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Student Fallacy (Why candidates pick this trap): Assumes the ball would already fall with terminal speed even when its density equals liquid density.
Note: When sigma = rho, buoyancy completely balances weight; terminal sinking speed must be zero.
3 Option (3)
✗ Incorrect Verdict & Scientific Reason:
Neglects buoyant upthrust completely.
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Student Fallacy (Why candidates pick this trap): Plots v_t proportional to sigma without subtracting liquid density rho.
Note: Buoyant force reduces net driving weight: net force is proportional to (sigma - rho), not sigma alone.
4 Option (4)
✗ Incorrect Verdict & Scientific Reason:
Ignores dependence of driving weight on ball density.
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Student Fallacy (Why candidates pick this trap): Assumes terminal velocity is a fixed constant independent of sphere mass.
Note: Heavier spheres of the same size sink faster through viscous drag.
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NTA Trap Alert: Neglecting Buoyant Upthrust (The Origin Extrapolation Trap)
Students who forget Archimedes' principle assume v_t ~ sigma and pick Graph (3), which passes through the origin.
🛡️ How to avoid the -1 mark: Always remember: In any fluid motion, effective weight is ALWAYS (sigma - rho)*V*g. The driving term is (sigma - rho), so velocity is zero when sigma = rho.
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Core NEET Syllabus Standard
NEET UG Physics Core Standards · Mechanical Properties of Fluids Standard Benchmark
Core Scientific Principle Tested:
"Terminal velocity of a spherical body falling in a fluid: v_t = (2/9)*(r^2*g/eta)*(sigma - rho). Sinking occurs only when sigma > rho."
Syllabus Focus: Stokes' Law, Terminal Velocity, and Practical Measurement of Viscosity
✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗