Q.45 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 45 Solution

Topic: Laws of Motion · Official NTA Booklet Code G5

Question

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (g = 10 m s⁻²).

✓

Verified Against NTA Final Answer Key

Option (4) : 1.5 m s⁻²

📚 Laws of Motion Easy

📋 Given Parameters & Problem Setup

Coefficient of static friction (μ_s) 0.15

Acceleration due to gravity (g) 10 m s⁻²

Limiting static friction force (f_s,max) μ_s N = μ_s m g

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The 30-Second Exam Hall Shortcut: ⚡ Limiting Acceleration Formula: a_max = μ_s g

⏱️ Save ~30 seconds

Static friction provides the acceleration: m a_max = μ_s m g ⟹ a_max = μ_s g = 0.15 × 10 = 1.5 m s⁻² in 5 seconds!

1 In the ground frame, static friction is the sole horizontal force accelerating the body: f_s = m a.

2 The maximum static friction available is f_s,max = μ_s N = μ_s m g.

3 For the body to remain stationary relative to the car, required acceleration cannot exceed available friction:

4 m a_max = μ_s m g ⟹ a_max = μ_s g.

5 Substitute given numbers: a_max = 0.15 × 10 m/s² = 1.5 m s⁻².

6 Lock Option (4) 1.5 m s⁻² immediately!

🛡️

Why You Can 100% Trust This Shortcut: Newtonian Mechanics · Static Friction Laws (The maximum acceleration a body can experience due to horizontal friction alone is a_max = μ_s g).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Free-Body Diagram in the Non-Inertial Reference Frame of the Car

Consider the reference frame of the accelerating car (acceleration a). In this accelerated frame, a pseudo-force F_pseudo = m a acts on the body in the direction opposite to the car’s acceleration. To prevent the body from slipping backward, static friction f_s acts forward:

F_{\text{pseudo}} = m a, \qquad f_s \ge F_{\text{pseudo}}

Step 2

Vertical Equilibrium and Normal Reaction

In the vertical direction, the body is in static equilibrium under gravity and the normal reaction from the car floor:

\sum F_y = 0 \implies N = m g

Step 3

Limiting Static Friction and Maximum Acceleration Condition

The maximum static friction that the floor can exert on the body is given by Amontons-Coulomb’s law of friction:

f_{s,\max} = \mu_s N = \mu_s m g

Step 4

Evaluation of Maximum Permissible Acceleration

Equating the pseudo force to the limiting static friction to determine a_max:

m a_{\max} = \mu_s m g \implies a_{\max} = \mu_s g = 0.15 \times 10 = 1.5\text{ m s}^{-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)

✗ Incorrect

Verdict & Scientific Reason:

Physically impossible value (candidate divided by friction coefficient or manipulated numbers).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate calculated g / (0.15 × 2) = 33 or 50.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect multiplier.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate multiplied by 8 or made an arithmetic error.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Off by two orders of magnitude (factor of 100).

⚠️

Student Fallacy (Why candidates pick this trap): Decimal point misplaced: 0.15 × 1000 = 150.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate maximum acceleration: a_max = μ_s g = 0.15 × 10 = 1.5 m s⁻².

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Why this is airtight: None. Candidate executed the standard friction relation correctly.

⚠️

NTA Trap Alert: Confusing Mass Dependence

Some candidates worry about the missing mass m of the body. Notice mass CANCELS identically: m a = μ_s m g ⟹ a = μ_s g. The maximum acceleration is completely mass-independent!

🛡️ How to avoid the -1 mark: Whenever horizontal friction accelerates a body, mass always cancels: a_max = μ_s g.

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Laws of Motion Standard Benchmark

Core Scientific Principle Tested:

"Limiting acceleration without slipping on a horizontal surface is a_max = μ_s g."

Syllabus Focus: Static and Limiting Friction

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 45 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Limiting Acceleration Formula: a_max = μ_s g

Step-by-Step Rigorous Workflow & Mathematical Proof

Free-Body Diagram in the Non-Inertial Reference Frame of the Car

Vertical Equilibrium and Normal Reaction

Limiting Static Friction and Maximum Acceleration Condition

Evaluation of Maximum Permissible Acceleration

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Mass Dependence

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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