Physics · Gravitation · NEET
| Full name | Universal gravitational constant | Acceleration due to gravity |
| Symbol | G (capital) | g (small) |
| Value | 6.67×10⁻¹¹ (fixed everywhere) | ≈ 9.8 m/s² at Earth's surface (varies) |
| Units | N m² kg⁻² | m/s² |
| Dimensions | [M⁻¹L³T⁻²] | [M⁰L¹T⁻²] |
| Depends on | Nothing — universal constant | Mass, radius, height, depth of body |
| Vector or scalar | Scalar constant | Vector (has direction, toward centre) |
No. Small g (acceleration due to gravity) tells you how fast a freely falling body speeds up, about 9.8 m/s² near Earth. Big G is the universal gravitational constant that appears in Newton's force law F = G·m₁m₂/r². They are different quantities with different meanings, values, and units. They are connected by the formula g = GM/R², where M and R are the mass and radius of the planet.
G is a fundamental constant of nature, so it has the same value everywhere in the universe: 6.67×10⁻¹¹ N m² kg⁻². Small g depends on the mass M and radius R of the body you are standing on, and on your height or depth, because g = GM/R². Change the planet, go higher, or go into a mine, and M/R² changes, so g changes. That is why g on the Moon (1.6 m/s²) is much less than g on Earth (9.8 m/s²).
On the surface of a planet of mass M and radius R, the two are linked by g = GM/R². For Earth this gives g ≈ 9.8 m/s². You can also rearrange it to find a planet's mass: M = gR²/G. This is exactly how Earth's mass is estimated, using g = 9.8 m/s², R = 6.4×10⁶ m and G = 6.67×10⁻¹¹.
No. G is the same everywhere, on the Moon, on Mars, and anywhere in space. Only g changes from planet to planet because g = GM/R² depends on that body's mass and radius. Students often wrongly think G is smaller on the Moon; it is g that is smaller, not G.
Small g is an acceleration, so its unit is m/s² and its dimensional formula is [M⁰L¹T⁻²] (written [LT⁻²]). Big G has unit N m² kg⁻² (same as m³ kg⁻¹ s⁻²) and dimensional formula [M⁻¹L³T⁻²]. NEET has directly asked the dimensions of G, so memorise [M⁻¹L³T⁻²].
If the mass of the Sun were ten times smaller and the universal gravitational constant G ten times larger, which statement is NOT correct?
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].
Try the real previous-year questions from this chapter — each with the answer and a full solution.
9.8 is the value of small g, the acceleration due to gravity at Earth's surface, in units of m/s². Big G has the much smaller numerical value 6.67×10⁻¹¹ N m² kg⁻².
G = 6.67×10⁻¹¹ N m² kg⁻² (equivalently m³ kg⁻¹ s⁻²). It is a universal constant, the same on Earth, on the Moon, and everywhere in the universe.
Yes. g is zero at the centre of the Earth and effectively zero far out in deep space, but G stays fixed at 6.67×10⁻¹¹ everywhere. G is a constant of nature; g is a value that depends on location.
Yes, in dimensions and meaning. Gravitational field intensity is force per unit mass, which equals the acceleration g and has the same dimensions [LT⁻²]. Near Earth's surface it equals 9.8 N/kg = 9.8 m/s².
Both use the same letter and both appear in gravitation formulas like g = GM/R². The quick fix: G is the fixed universal constant in Newton's law of gravitation, while g is the changing local acceleration you feel on a particular planet at a particular height.
