Q.2 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 2 Solution

Topic: Mechanical Properties of Fluids · Official NTA Booklet Code M1

Question

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d, then the viscous force acting on the ball will be:

✓

Verified Against NTA Final Answer Key

Option (1) : Mg / 2

📚 Mechanical Properties of Fluids Easy

📋 Given Parameters & Problem Setup

Mass of Ball M

Density of Ball d

Density of Glycerine d / 2

Kinematic Condition Velocity is constant (terminal velocity)

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The 30-Second Exam Hall Shortcut: ⚡ Terminal Equilibrium: F_v = Weight - Upthrust

⏱️ Save ~20 seconds

At terminal velocity, acceleration is zero: $W = F_B + F_v$ . Since liquid density is half of ball density ( $d_L = d/2$ ), the buoyant force is exactly half of the ball weight ( $F_B = W/2$ ). Thus, the viscous force must support the other half: $F_v = W - W/2 = Mg/2$ ! Match Option (1)!

1 Constant velocity

\implies a = 0 \implies

net vertical force

= 0

2 Weight acting downward:

W = Mg

3 Upward buoyant force:

F_B = \frac{\rho_L}{\rho} Mg = \frac{d/2}{d} Mg = \frac{Mg}{2}

4 Upward viscous force:

F_v = W - F_B = Mg - \frac{Mg}{2} = \frac{Mg}{2}

5 Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Newton's first law of motion and Archimedes' principle for terminal steady state.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating the Equilibrium Condition at Terminal Velocity

When the small sphere attains a constant terminal velocity ( $v_t$ ), its downward acceleration is zero ( $a = 0$ ). By Newton's second law, the downward gravitational force is perfectly balanced by the sum of upward buoyant force ( $F_B$ ) and upward viscous drag ( $F_v$ ):

\Sigma F_y = 0 \implies W = F_B + F_v \implies F_v = W - F_B

Step 2

Calculating Weight and Buoyant Force

Let $V$ be the volume of the sphere. The mass is $M = V \cdot d$ , so $V = M / d$ . The weight is $W = Mg$ . The buoyant force exerted by glycerine of density $\rho_L = d/2$ is:

F_B = V \cdot \rho_L \cdot g = \left(\frac{M}{d}\right) \left(\frac{d}{2}\right) g = \frac{Mg}{2}

Step 3

Determining the Viscous Force

Substitute $W = Mg$ and $F_B = Mg/2$ into the force balance equation:

F_v = Mg - \frac{Mg}{2} = \frac{Mg}{2}

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360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✓ 100% Correct

Verdict & Scientific Reason:

Exact balance of forces: Viscous force = Weight - Buoyant force = Mg - Mg/2 = Mg/2.

💡

Why this is airtight: None; textbook equilibrium derivation.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Ignores the buoyant force completely ( $F_B = 0$ ), which is only valid in vacuum.

⚠️

Student Fallacy (Why candidates pick this trap): Equating viscous force directly to gravitational weight without subtracting upthrust.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Incorrectly adds buoyant force to weight ( $W + F_B = Mg + Mg/2 = 3Mg/2$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Adding forces in the wrong direction instead of subtracting upward buoyant force.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Inverts density ratio and adds unphysical multipliers.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by density ratio inverse.

⚠️

NTA Trap Alert: Forgetting Archimedes Upthrust in Viscous Fluid Trap

Students often memorize Stokes' law ( $6\pi\eta r v$ ) and assume the viscous force equals $Mg$ directly, forgetting that the fluid also exerts a hydrostatic buoyant force that carries half the weight.

🛡️ How to avoid the -1 mark: Always draw the FBD: Downward =

Mg

; Upward =

F_B + F_v

. At constant speed,

F_v = Mg - F_B

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Core NEET Syllabus Standard

NCERT Physics · Mechanical Properties of Fluids Standard Benchmark

Core Scientific Principle Tested:

"At terminal velocity, the net downward force on a falling body is zero: Viscous force equals weight minus buoyant force ( $F_v = W - F_B$ )."

Syllabus Focus: Stokes' Law and Terminal Velocity

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 2 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Terminal Equilibrium: F_v = Weight - Upthrust

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating the Equilibrium Condition at Terminal Velocity

Calculating Weight and Buoyant Force

Determining the Viscous Force

360° Option Elimination Engine Key Feature

NTA Trap Alert: Forgetting Archimedes Upthrust in Viscous Fluid Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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