The dimensional formula of the gravitational constant G is [M⁻¹L³T⁻²], and the ratio E/G (energy divided by G) has the dimensions [M²L⁻¹T⁰]. To get G, rearrange Newton's law F = G·m₁m₂/r² into G = F·r²/(m₁m₂). Memory hook: G is the only common mechanical quantity that carries M⁻¹ (a "one-over-mass"), so E/G brings in an extra mass and gives M².
Left: G is derived by rearranging Newton's law of gravitation to G = F·r²/(m₁m₂), giving [M⁻¹L³T⁻²]. Right: dividing energy [ML²T⁻²] by G subtracts the powers to give E/G = [M²L⁻¹T⁰], the NEET 2021 answer.
Your doubts, answered
How do I derive the dimensions of G from Newton's law of gravitation?
Start from F = G·m₁m₂/r². Make G the subject: G = F·r²/(m₁m₂). Now put the dimensions of each part. Force F = [MLT⁻²], r² = [L²], and m₁m₂ = [M²]. So G = [MLT⁻²]·[L²] / [M²] = [M¹⁻² L¹⁺² T⁻²] = [M⁻¹L³T⁻²]. That is the dimensional formula of the gravitational constant.
What is the dimension of E/G and how is it found?
Energy E = [ML²T⁻²] (same as work = force × distance). Gravitational constant G = [M⁻¹L³T⁻²]. Divide: E/G = [ML²T⁻²] / [M⁻¹L³T⁻²]. Subtract powers: M → 1 − (−1) = 2, L → 2 − 3 = −1, T → −2 − (−2) = 0. So E/G = [M²L⁻¹T⁰]. This is the exact NEET 2021 answer.
Is G (gravitational constant) the same as g (acceleration due to gravity)?
No. They are different and NEET loves to test this. Big G is the universal gravitational constant with dimensions [M⁻¹L³T⁻²] and unit N·m²/kg². Small g is acceleration due to gravity with dimensions [LT⁻²] and unit m/s². Small g changes with location; big G is the same everywhere in the universe.
Why does the gravitational constant carry M⁻¹ (one over mass)?
Because in G = F·r²/(m₁m₂), you divide force by the product of two masses (M²) but multiply back only one mass through force ([MLT⁻²]). Net mass power = 1 − 2 = −1. G is in fact the standard NEET example of a mechanical quantity whose dimension of mass is M⁻¹ (asked directly in NEET 2023).
What are the dimensions of gravitational potential energy, potential and intensity?
These are tested together (NEET 2022 match list). Gravitational potential energy = [ML²T⁻²] (it is just energy). Gravitational potential (energy per unit mass) = [L²T⁻²]. Gravitational intensity or field (force per unit mass, same as g) = [LT⁻²]. Only G itself is [M⁻¹L³T⁻²].
⚠️ The NEET trap ✗ Writing G = [MLT⁻²] or [M¹L³T⁻²] by copying force or forgetting to divide by the two masses. ✓ G = F·r²/(m₁m₂) = [MLT⁻²]·[L²]/[M²] = [M⁻¹L³T⁻²]. The mass power must be negative because you divide by two masses. 🧠 G is the M⁻¹ quantity. If your G has a positive mass power, you skipped dividing by m₁m₂.
Real NEET questions
NEET 2021
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of:
A · [M][L⁰][T⁰]
B · [M²][L⁻²][T⁻¹]
C · [M²][L⁻¹][T⁰] ✓
D · [M][L⁻¹][T⁻¹]
Solution: Step 1: Energy E = [ML²T⁻²]. Step 2: Gravitational constant G = [M⁻¹L³T⁻²]. Step 3: Divide, E/G = [ML²T⁻²] / [M⁻¹L³T⁻²]. Step 4: Subtract powers — M: 1−(−1)=2, L: 2−3=−1, T: −2−(−2)=0. Result E/G = [M²L⁻¹T⁰]. Answer C.
NEET 2022
Match List-I with List-II: (a) Gravitational constant G (b) Gravitational potential energy (c) Gravitational potential (d) Gravitational intensity, with (i) [L²T⁻²] (ii) [M⁻¹L³T⁻²] (iii) [LT⁻²] (iv) [ML²T⁻²].
A · (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
B · (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii) ✓
C · (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
D · (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)
Solution: G = F·r²/(m₁m₂) = [M⁻¹L³T⁻²] → (ii). Gravitational PE is energy = [ML²T⁻²] → (iv). Gravitational potential = PE per unit mass = [ML²T⁻²]/[M] = [L²T⁻²] → (i). Gravitational intensity = force per unit mass = [MLT⁻²]/[M] = [LT⁻²] → (iii). So (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii). Answer B.
NEET 2023
The mechanical quantity which has dimensions of the reciprocal of mass (M⁻¹) is:
A · Torque
B · Gravitational constant ✓
C · Angular momentum
D · Coefficient of thermal conductivity
Solution: Check the mass power of each. Torque = [ML²T⁻²] (M¹). Angular momentum = [ML²T⁻¹] (M¹). Thermal conductivity = [MLT⁻³K⁻¹] (M¹). Gravitational constant G = [M⁻¹L³T⁻²] has mass power M⁻¹. So G is the reciprocal-of-mass quantity. Answer B.
Solved Units And Measurements NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the dimensional formula of gravitational constant G?
The dimensional formula of the gravitational constant is [M⁻¹L³T⁻²]. It comes from G = F·r²/(m₁m₂) = [MLT⁻²]·[L²]/[M²].
What is the SI unit of gravitational constant G?
The SI unit of G is newton metre squared per kilogram squared, written N·m²/kg² (equivalently m³·kg⁻¹·s⁻²). Its numerical value is 6.674 × 10⁻¹¹ N·m²/kg².
What is the dimension of E/G?
E/G has dimensions [M²L⁻¹T⁰], which is the same as [M²L⁻¹]. This is a direct NEET 2021 question.
Does gravitational constant have M⁻¹ in its dimensions?
Yes. G = [M⁻¹L³T⁻²]. It is the standard NEET example of a mechanical quantity with a reciprocal-of-mass (M⁻¹) dimension, asked directly in NEET 2023.
How is G different from g?
Big G is the universal gravitational constant, [M⁻¹L³T⁻²], constant everywhere. Small g is acceleration due to gravity, [LT⁻²], and changes with height and location.
