Q.35 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 35 Solution

Topic: Units and Measurements · Official NTA Booklet Code M1

Question

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

✓

Verified Against NTA Final Answer Key

Option (2) : [F] [A] [T^2]

📚 Units and Measurements Easy

📋 Given Parameters & Problem Setup

Fundamental Base Quantities Force [F], Acceleration [A], Time [T]

Target Derived Quantity Energy [E]

⚡

The 30-Second Exam Hall Shortcut: ⚡ Work = Force × Distance, and Distance = 1/2 A T²

⏱️ Save ~20 seconds

Energy has dimensions of Work: $[E] = [F] \times [\text{Displacement}]$ . From kinematics, displacement $s = \frac{1}{2} a t^2 \implies [s] = [A][T^2]$ . Therefore, $[E] = [F][A][T^2]$ ! Instant 5-second calculation matching Option (2)!

1 Recall physical definition of work/energy:

\text{Energy} = \text{Force} \times \text{Displacement}

2 Express displacement

[s]

in terms of acceleration

[A]

and time

[T]

s = \frac{1}{2} a t^2 \implies [s] = [A] [T^2]

3 Substitute:

[E] = [F] [s] = [F] [A] [T^2]

4 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical dimensional analysis and fundamental kinematic definitions.

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating the Dimensional Equation

Assume the dimensional formula of energy in terms of $[F]$ , $[A]$ , and $[T]$ is given by:

[E] = [F]^x [A]^y [T]^z

Step 2

Substituting Fundamental Dimensions in SI Base Units

The standard SI dimensional formulae for the quantities are: - $[E] = [M^1 L^2 T^{-2}]$ - $[F] = [M^1 L^1 T^{-2}]$ - $[A] = [M^0 L^1 T^{-2}]$ - $[T] = [T^1]$

[M^1 L^2 T^{-2}] = [M^1 L^1 T^{-2}]^x [L^1 T^{-2}]^y [T^1]^z = [M^x L^{x+y} T^{-2x - 2y + z}]

Step 3

Solving for Exponents x, y, and z

Equating powers of $M$ , $L$ , and $T$ on both sides: 1. Power of $M$ : $x = 1$ 2. Power of $L$ : $x + y = 2 \implies 1 + y = 2 \implies y = 1$ 3. Power of $T$ : $-2x - 2y + z = -2 \implies -2(1) - 2(1) + z = -2 \implies -4 + z = -2 \implies z = 2$

x = 1, \quad y = 1, \quad z = 2 \implies [E] = [F^1 A^1 T^2]

⭐

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:

Dimensions of impulse or momentum, not energy ( $[F][A][T] = [M L T^{-2}][L T^{-2}][T] = [M L^2 T^{-3}]$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Linear time dependence error.

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Exact dimensional formula of energy: $[F][A][T^2] = [M L T^{-2}][L T^{-2}][T^2] = [M L^2 T^{-2}]$ .

💡

Why this is airtight: None; flawless dimensional equivalence.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Incorrect negative power of time.

⚠️

Student Fallacy (Why candidates pick this trap): Conflating frequency with time.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Dimensions of mass $\times$ time ( $[F/A][T] = [M][T]$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Incorrect exponent inversion.

⚠️

NTA Trap Alert: Power of Time Error Trap

Students who remember $[s] = [A][T^2]$ sometimes write $[E] = [F][A][T]$ (Option 1) by confusing velocity ( $v = at$ ) with displacement ( $s = \frac{1}{2}at^2$ ).

🛡️ How to avoid the -1 mark: Check dimensions:

[F][A][T^2] = (\text{Force}) \times (\text{Displacement}) = \text{Energy}

📖

Core NEET Syllabus Standard

NCERT Physics · Units and Measurements Standard Benchmark

Core Scientific Principle Tested:

"The principle of homogeneity of dimensions ensures that physical equations can be converted to any system of fundamental units."

Syllabus Focus: Dimensional Analysis and Its Applications

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 35 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Work = Force × Distance, and Distance = 1/2 A T²

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating the Dimensional Equation

Substituting Fundamental Dimensions in SI Base Units

Solving for Exponents x, y, and z

360° Option Elimination Engine Key Feature

NTA Trap Alert: Power of Time Error Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Units and Measurements

Vernier Calliper Negative Zero Error & Full Marks Bonus Audit

Dimensional Analysis of Combined Thermal Radiation Constants (sigma_s * k_B^-1 * b)

Vernier Callipers Least Count, Positive Zero Error & Corrected Reading

Percentage Error in Physical Quantity P = a³ b² / (c √d)

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