Q.25 Physics ⭐ 360° Option Elimination Active

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NEET 2021 Physics Question 25 Solution

Topic: Units and Measurements · Official NTA Booklet Code M1

Question

If E and G respectively denote energy and gravitational constant, then E has the dimensions of:

✓

Verified Against NTA Final Answer Key

Option (1) : [M^2] [L^-1] [T^0]

📚 Units and Measurements Easy

📋 Given Parameters & Problem Setup

E Energy

G Universal Gravitational Constant

⚡

The 30-Second Exam Hall Shortcut: ⚡ Dimensional Quotient: [E] / [G]

⏱️ Save ~20 seconds

$[E] = [M L^2 T^{-2}]$ and $[G] = [M^{-1} L^3 T^{-2}]$ . Divide them: $[E/G] = \frac{[M L^2 T^{-2}]}{[M^{-1} L^3 T^{-2}]} = [M^{1 - (-1)} L^{2 - 3} T^{-2 - (-2)}] = [M^2 L^{-1} T^0]$ ! Instant 10-second calculation matching Option (1)!

1 Dimensional formula of Energy:

[E] = [M^1 L^2 T^{-2}]

2 Dimensional formula of

G

: From

F = \frac{G m^2}{r^2} \implies G = \frac{F r^2}{m^2} \implies [G] = \frac{[M L T^{-2}][L^2]}{[M^2]} = [M^{-1} L^3 T^{-2}]

3 Compute

[E/G] = \frac{[M L^2 T^{-2}]}{[M^{-1} L^3 T^{-2}]}

4 Exponents:

M: 1 - (-1) = 2

;

L: 2 - 3 = -1

;

T: -2 - (-2) = 0

5 Result:

[M^2 L^{-1} T^0] \implies

Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical dimensional homogeneity and definition of fundamental physical constants.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Deriving the Dimensions of Energy (E)

Energy has the dimensions of work (Force $\times$ Displacement):

[E] = [\text{Work}] = [\text{Force}] \times [\text{Displacement}] = [M L T^{-2}] \times [L] = [M^1 L^2 T^{-2}]

Step 2

Deriving the Dimensions of Gravitational Constant (G)

From Newton's universal law of gravitation $F = G \frac{m_1 m_2}{r^2}$ :

G = \frac{F \cdot r^2}{m_1 m_2} \implies [G] = \frac{[M L T^{-2}] \times [L^2]}{[M] \times [M]} = \frac{[M L^3 T^{-2}]}{[M^2]} = [M^{-1} L^3 T^{-2}]

Step 3

Computing the Dimensions of the Ratio E / G

Divide the dimensional formula of $E$ by that of $G$ using the laws of indices:

\left[\frac{E}{G}\right] = \frac{[M^1 L^2 T^{-2}]}{[M^{-1} L^3 T^{-2}]} = [M^{1 - (-1)} L^{2 - 3} T^{-2 - (-2)}] = [M^2 L^{-1} T^0]

⭐

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 dimensional formula of the ratio $E/G$ .

💡

Why this is airtight: None; textbook dimensional analysis.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Dimensions of coefficient of viscosity ( $eta$ ), not $E/G$ .

⚠️

Student Fallacy (Why candidates pick this trap): Confusing

E/G

with viscosity dimensions.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Dimensions of pure mass ( $[M]$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Arithmetic cancellation error resulting in

[M]

4 4

✗ Incorrect

Verdict & Scientific Reason:

Incorrect power of length and time.

⚠️

Student Fallacy (Why candidates pick this trap): Failing to cancel

T^{-2}

in numerator and denominator.

⚠️

NTA Trap Alert: Time Dimension Cancellation Trap

Both $[E]$ and $[G]$ contain $T^{-2}$ in their dimensions. In the quotient $E/G$ , the time terms cancel out completely to give $T^0$ . Students who forget that $T^{-2} / T^{-2} = T^0$ get trapped by Option (4).

🛡️ How to avoid the -1 mark: Notice that

T^{-2}

is in both

E

and

G

-2 - (-2) = 0 \implies T^0

📖

Core NEET Syllabus Standard

NCERT Physics · Units and Measurements Standard Benchmark

Core Scientific Principle Tested:

"Dimensional formulae of derived physical quantities are obtained by algebraic substitution and laws of indices of base dimensions $[M]$ , $[L]$ , and $[T]$ ."

Syllabus Focus: Dimensional Analysis and Its Applications

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 25 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Dimensional Quotient: [E] / [G]

Step-by-Step Rigorous Workflow & Mathematical Proof

Deriving the Dimensions of Energy (E)

Deriving the Dimensions of Gravitational Constant (G)

Computing the Dimensions of the Ratio E / G

360° Option Elimination Engine Key Feature

NTA Trap Alert: Time Dimension Cancellation 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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