Q.47 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 47 Solution

Topic: Electrostatic Potential and Capacitance · Official NTA Booklet Code M1

Question

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

✓

Verified Against NTA Final Answer Key

Option (4) : 1980 V

📚 Electrostatic Potential and Capacitance Easy

📋 Given Parameters & Problem Setup

Number of Small Drops (n) 27

Potential of Each Small Drop (v) 220 V

⚡

The 30-Second Exam Hall Shortcut: ⚡ Coalescence Potential Scaling: V = n^(2/3) v

⏱️ Save ~20 seconds

For $n$ identical droplets combining into one larger drop, the potential scales as $V = n^{2/3} v$ . Here $n = 27 = 3^3$ , so $n^{2/3} = (3^3)^{2/3} = 3^2 = 9$ . The big drop potential is $V = 9 \times 220\text{ V} = 1980\text{ V}$ ! Instant 5-second calculation matching Option (4)!

1 Recall universal droplet scaling formula:

V = n^{2/3} v

2 Here

n = 27

and

v = 220\text{ V}

3 Compute factor:

27^{2/3} = (27^{1/3})^2 = 3^2 = 9

4 Big drop potential:

V = 9 \times 220\text{ V} = 1980\text{ V}

5 Match Option (4).

🛡️

Why You Can 100% Trust This Shortcut: Canonical volume conservation (

R = n^{1/3} r

) and charge conservation (

Q = n q

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Conservation of Volume

Let $r$ be the radius of each small drop and $R$ be the radius of the combined bigger drop. Since the liquid is incompressible, the total volume is conserved:

\frac{4}{3}\pi R^3 = n \left(\frac{4}{3}\pi r^3\right) \implies R^3 = 27 r^3 \implies R = (27)^{1/3} r = 3r

Step 2

Conservation of Electric Charge

Let $q$ be the charge on each small drop. Total charge is conserved upon coalescence:

Q = n q = 27 q

Step 3

Calculating the Potential of the Bigger Drop

The potential of a single small conducting droplet of radius $r$ and charge $q$ is $v = \frac{kq}{r} = 220\text{ V}$ . The potential of the big drop is:

V = \frac{kQ}{R} = \frac{k(27q)}{3r} = \frac{27}{3} \left(\frac{kq}{r}\right) = 9 v

Step 4

Numerical Evaluation

Substitute $v = 220\text{ V}$ :

V = 9 \times 220\text{ V} = 1980\text{ V}

⭐

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

✗ Incorrect

Verdict & Scientific Reason:

Result of multiplying by $n^{1/3} = 3$ ( $3 \times 220 = 660\text{ V}$ ), which represents the radius expansion, not potential.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by

R/r = 3

instead of

Q/R = 9

2 2

✗ Incorrect

Verdict & Scientific Reason:

Result of multiplying by 6 arbitrarily.

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic miscalculation.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Computational estimation error.

⚠️

Student Fallacy (Why candidates pick this trap): Calculation error.

4 4

✓ 100% Correct

Verdict & Scientific Reason:

Exact electrostatic potential of the big drop: $V = n^{2/3} v = 9 \times 220 = 1980\text{ V}$ .

💡

Why this is airtight: None; flawless droplet coalescence solution.

⚠️

NTA Trap Alert: Linear Charge vs. Potential Scaling Trap

Students who assume potential scales directly with charge ( $Q = 27q$ ) get $27 \times 220 = 5940\text{ V}$ , forgetting that the capacitance also increases by a factor of $3$ ( $R = 3r$ ), so the potential increases by only $27/3 = 9$ .

🛡️ How to avoid the -1 mark: Use the master formula:

V = n^{2/3} v

. For

n = 27

, multiplier is

27^{2/3} = 9

📖

Core NEET Syllabus Standard

NCERT Physics · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"For coalescing droplets, volume conservation gives $R = n^{1/3} r$ and potential scales as $V = n^{2/3} v$ ."

Syllabus Focus: Potential Due to a Charged Sphere

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 47 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Coalescence Potential Scaling: V = n^(2/3) v

Step-by-Step Rigorous Workflow & Mathematical Proof

Conservation of Volume

Conservation of Electric Charge

Calculating the Potential of the Bigger Drop

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Linear Charge vs. Potential Scaling Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Electrostatic Potential and Capacitance

Electrostatic Energy Ratio in a Series-Parallel Capacitor Network

Path-Independence of Electrostatic Work & Potential of a Uniformly Charged Sphere

Electrostatic Shielding and Cavity Field with Interior Point Charge

Speed of an Attracted Point Charge Reaching the Surface of a Charged Insulating Sphere

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