Q.41 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 41 Solution

Topic: Laws of Motion · Official NTA Booklet Code 50

Question

A car travels on a circular racetrack of radius 50 m, which is banked at an angle θ. If the car travels at a speed 10 m s⁻¹, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 m s⁻², the value of θ is:

✓

Verified Against NTA Final Answer Key

Option (1) : theta = tan^-1(1/5)

📚 Laws of Motion Easy

📋 Given Parameters & Problem Setup

Track Radius r = 50 m

Speed of Car v = 10 m/s

Acceleration due to Gravity g = 10 m/s^2

Condition Minimum wear and tear on tyres (zero friction required)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Optimum Banking Formula Shortcut

⏱️ Instant recall saves 45 seconds.

Zero wear and tear means zero sideways friction: tan(theta) = v^2 / (r * g)!

1 Substitute: v^2 = 10^2 = 100.

2 Denominator: r * g = 50 * 10 = 500.

3 tan(theta) = 100 / 500 = 1/5.

4 theta = tan^-1(1/5). Solved in 5 seconds!

🛡️

Why You Can 100% Trust This Shortcut: When wear and tear is minimum, the horizontal component of the normal reaction N*sin(theta) provides 100% of the centripetal force m*v^2/r, while N*cos(theta) balances gravity m*g, giving tan(theta) = v^2 / (rg).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Understand the Physical Meaning of "Minimum Wear and Tear"

Tyre wear and tear occurs due to sideways frictional forces between the tyres and the road surface:

f = 0 \quad (\text{Ideal / Optimum Banking Condition})

• When a vehicle travels at the design speed on a banked road, no lateral friction is demanded.
• Centripetal acceleration is supplied entirely by the normal force from the inclined road surface.

Step 2

Set Up Dynamic Equilibrium Equations

Resolve the normal force N into horizontal and vertical components:

N \sin\theta = \frac{m v^2}{r}, \qquad N \cos\theta = m g

• N*sin(theta) acts toward the center of the circular track.
• N*cos(theta) balances the vehicle weight.

Step 3

Divide Equations and Solve for theta

Divide the horizontal balance by the vertical balance:

\tan\theta = \frac{v^2}{r g} = \frac{10^2}{50 \times 10} = \frac{100}{500} = \frac{1}{5} \implies \theta = \tan^{-1}\left(\frac{1}{5}\right)

• Matches Option (1) exactly.

⭐

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 Option (1)

✓ 100% Correct

Verdict & Scientific Reason:

100% mathematically exact; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Direct application of optimum banking angle formula tan(theta) = v^2 / (rg).

Note: Flawless physics.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic factor of 2 error.

⚠️

Student Fallacy (Why candidates pick this trap): Uses r = 25 or multiplies numerator by 2.

Note: v^2 / (rg) = 100 / 500 = 1/5.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Confuses with 30 or 60 degree standard angles.

⚠️

Student Fallacy (Why candidates pick this trap): Attempts to force a special triangle angle.

Note: Banking angles are derived from parameters, not standard trigonometry.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Inverted and multiplied.

⚠️

Student Fallacy (Why candidates pick this trap): Arbitrary distractor.

Note: tan(theta) = 1/5.

⚠️

NTA Trap Alert: Confusing Optimum Speed with Maximum Friction Speed

Students who look for friction coefficient mu panic because mu is not given in the question.

🛡️ How to avoid the -1 mark: Remember: The phrase "wear and tear is minimum" ALWAYS means friction is ZERO! Set f = 0 ==> tan(theta) = v^2 / (rg).

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Laws of Motion Standard Benchmark

Core Scientific Principle Tested:

"Optimum banking angle of a circular road: tan(theta) = v^2 / (r*g). At this speed, a vehicle can navigate the turn safely even on frictionless ice."

Syllabus Focus: Circular Motion & Banking of Curved Roads

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 41 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Optimum Banking Formula Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Understand the Physical Meaning of "Minimum Wear and Tear"

Set Up Dynamic Equilibrium Equations

Divide Equations and Solve for theta

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Optimum Speed with Maximum Friction Speed

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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