Universal Gravitational Constant G: Value, Units, and Dimensions
Physics · Gravitation · NEET
The universal gravitational constant G is a fixed number that appears in Newton's law of gravitation, F = G m1 m2 / r^2. Its value is G = 6.674 x 10^-11 N m^2/kg^2, its SI unit is N m^2 kg^-2, and its dimensional formula is [M^-1 L^3 T^-2]. Memory hook: G is the only "-1" power on mass in gravitation, so remember it as "one over M, times L cubed, over T squared."
Two masses m1 and m2 separated by distance r attract each other with equal and opposite forces F. The constant G in F = G m1 m2 / r^2 is the same everywhere in the universe, with value 6.674 x 10^-11 N m^2/kg^2 and dimensions [M^-1 L^3 T^-2].
Your doubts, answered
Is G really the same everywhere in the universe?
Yes. G is a universal constant, which means it has the same value at every point in space and time, on Earth, on the Moon, or near a distant star. This is different from g (acceleration due to gravity), which changes from planet to planet and with height. For NEET, remember: G never changes, g changes. The value G = 6.674 x 10^-11 N m^2/kg^2 is used everywhere.
Why is G such a tiny number (10^-11)?
G is small because gravity itself is a very weak force between ordinary objects. Two 1 kg masses held 1 m apart pull on each other with a force of only about 6.67 x 10^-11 N, which is far too small to feel. Gravity only becomes strong when one mass is huge, like the Earth. This tiny value is why we do not see everyday objects sticking together by gravity.
How do I get the units of G from the formula?
Start from F = G m1 m2 / r^2 and solve for G: G = F r^2 / (m1 m2). Put in the units: force is N (newton), r^2 is m^2, and m1 m2 is kg^2. So the unit of G = N x m^2 / kg^2 = N m^2 kg^-2. This is the SI unit. NEET often asks you to derive this, so always start from the rearranged formula.
How do I derive the dimensional formula of G?
Use G = F r^2 / (m1 m2). Force F has dimensions [M L T^-2], r^2 has [L^2], and m1 m2 has [M^2]. So G = [M L T^-2] x [L^2] / [M^2] = [M^(1-2) L^(1+2) T^-2] = [M^-1 L^3 T^-2]. The mass power comes out as -1, which is the key clue that a dimension belongs to G.
Does the value of G change on the Moon or at a height?
No. G is a fundamental constant and stays 6.674 x 10^-11 N m^2/kg^2 on the Moon, at the top of a mountain, or in deep space. What changes with location and height is g, because g = GM/R^2 depends on the mass M and radius R of the body. Do not confuse a changing g with a fixed G.
⚠️ The NEET trap ✗ Picking [M L^3 T^-2] (mass power +1) for the dimensions of G, because students forget that the two masses in the denominator lower the mass power. ✓ The mass power is -1. Since G = F r^2 / (m1 m2), the two masses (M^2) sit in the denominator and one M from force partly cancels, giving [M^-1 L^3 T^-2]. 🧠 In any match-the-dimension question, the term with M to the power -1 is always G. NTA loves this in List-matching PYQs.
Solution: Step 1: G from G = F r^2 / (m1 m2) = [M L T^-2][L^2]/[M^2] = [M^-1 L^3 T^-2] = (ii). Step 2: Potential energy is work, so PE = [M L^2 T^-2] = (iv). Step 3: Gravitational potential is energy per unit mass = [M L^2 T^-2]/[M] = [L^2 T^-2] = (i). Step 4: Gravitational intensity is force per unit mass (same as acceleration) = [L T^-2] = (iii). So (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii). Answer: B.
2018
If the mass of the Sun were ten times smaller and the universal gravitational constant G ten times larger, which statement is NOT correct?
A · Time period of a simple pendulum on Earth would decrease
B · Walking on the ground would become more difficult
C · Raindrops will fall faster
D · 'g' on the Earth will not change ✓
Solution: Step 1: Acceleration due to gravity on Earth is g = G M_earth / R^2, which depends on G and the Earth's mass, not on the Sun's mass. Step 2: If G becomes 10 times larger, g on Earth becomes 10 times larger too. Step 3: So the statement 'g on the Earth will not change' is the incorrect one. Step 4: A larger g means the pendulum period T = 2 pi sqrt(L/g) decreases, walking gets harder, and raindrops fall faster, so those are all correct. Answer: D (the NOT correct statement).
Solved Gravitation NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the value of the universal gravitational constant G?
G = 6.674 x 10^-11 N m^2/kg^2 (often rounded to 6.67 x 10^-11 for NEET calculations). It was first measured accurately by Henry Cavendish.
What is the SI unit of G?
The SI unit of G is N m^2 kg^-2 (newton metre squared per kilogram squared). You get it by rearranging G = F r^2 / (m1 m2).
What is the dimensional formula of G?
The dimensional formula of G is [M^-1 L^3 T^-2]. The mass power is -1, which is the easiest way to spot G in dimension-matching questions.
What is the difference between G and g?
G is the universal gravitational constant and is the same everywhere. g is the acceleration due to gravity and changes with location, since g = GM/R^2. Their units and dimensions are completely different.
Why is G called a universal constant?
Because it has the same fixed value for every pair of masses anywhere in the universe. It does not depend on the type of matter, the medium between the masses, or the location.
