Newton's Universal Law of Gravitation: Statement and Formula

Physics · Gravitation · NEET

Newton's Universal Law of Gravitation says every two masses pull each other with a force F = G m1 m2 / r squared. The force grows with both masses and drops fast as distance grows (inverse-square). Memory hook: "More mass, more pull; more gap, much less pull" — double the distance and the force becomes one-fourth, not one-half.
Force between two masses: F = G m1 m2 / r squaredm1m2FFr (centre to centre)Equal and opposite (attractive)
Two masses m1 and m2 separated by centre-to-centre distance r attract each other with equal and opposite forces F = G m1 m2 / r squared. Doubling r makes F one-fourth.

Your doubts, answered

Is gravitational force between two masses attractive or repulsive?

It is always attractive. Any two masses pull each other toward one another along the straight line joining their centres. Gravity has no repulsive form, unlike electric charges. So in NEET problems the direction is always along the line joining the two bodies, pointing inward.

Why is it called the 'universal' law of gravitation?

Because the same formula F = G m1 m2 / r squared works everywhere and for everything — an apple and Earth, Earth and Moon, Sun and a planet, or two stars. The constant G has the same value in the whole universe. That universal reach is why NEET treats it as a single master law for the full Gravitation chapter.

Does the gravitational force depend on the medium between the two masses?

No. Unlike electric force, gravitational force does not change if you put air, water, glass, or vacuum between the masses. Only the two masses and the distance between their centres matter. This is a common one-line NEET fact, so remember: medium has no effect on gravity.

What happens to the force if the distance is doubled?

The force becomes one-fourth. Because F is proportional to 1 / r squared, if r becomes 2r then r squared becomes 4 r squared, so F drops to F/4. If distance triples, force becomes F/9. NEET loves this inverse-square scaling, so always square the distance ratio.

Is the force on the smaller mass equal to the force on the bigger mass?

Yes, equal in size and opposite in direction (Newton's third law). Earth pulls you with the same force you pull Earth. You accelerate a lot because your mass is tiny (a = F/m), while Earth barely moves because its mass is huge. Equal force, very different acceleration.

⚠️ The NEET trap
Thinking the force is proportional to 1/r, so doubling the distance halves the force.
The force follows 1 / r squared. Doubling the distance makes the force one-fourth (F/4), and tripling it makes the force one-ninth (F/9).
🧠 Square the distance first, then divide. r goes x2, force goes /4.

Real NEET questions

NEET 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: Surface gravity comes from the same universal law: g = G M_earth / R squared. It depends on G and Earth's mass, not on the Sun's mass. Step 2: Making G ten times larger makes g ten times larger, so g on Earth DOES change. Step 3: Therefore the statement 'g will not change' is the incorrect one. Step 4: A larger g means faster raindrops, a shorter pendulum period (T = 2 pi root(L/g)), and harder walking — all correct. Answer: D.

Solved Gravitation NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 27 Gravitation NEET PYQs ›
Next concept: Force Between Two MassesKeep learning — 2 minFeeling ready? Solve the Gravitation NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

What is the SI unit and value of G in the formula?

G is the universal gravitational constant. Its value is 6.67 x 10 to the power minus 11 and its SI unit is N m squared / kg squared. It is a fixed constant, the same everywhere in the universe.

Does the law work for large bodies like Earth and Moon?

Yes. For spheres like planets, we use the distance r between their centres. So Earth and Moon obey F = G m1 m2 / r squared with r as the centre-to-centre distance.

What is the difference between G and g?

G is the universal constant (6.67 x 10 to the minus 11, same everywhere). g is the acceleration due to gravity on a planet's surface (about 9.8 m/s squared on Earth) and changes from planet to planet. They are linked by g = G M / R squared.

Why don't we feel the gravity between two people sitting close?

Because the masses are tiny and G is extremely small. Two 60 kg people 1 m apart feel a force of only about 2 x 10 to the minus 7 N — far too weak to notice. Gravity becomes strong only when at least one mass is planet-sized.