State the universal law of gravitation

Scenario

Seb ka ped se girna toh sabne dekha hai — par Newton ne socha ki agar gravity seb ko neeche kheenchti hai, toh kya wahi force chand ko bhi kheeche rakhti hai?

Kya har cheez duniya mein har doosri cheez ko kheenchti hai — tum bhi apne bench ko?

Mental model

Har do cheezein ek doosre ko kheenchti hain — jitna bhaari, utni zyada kheench; jitna door, utni kam.

Sochlo do magnets hain — bade magnets zyada kheenchte hain, aur jaise-jaise door le jaao, pull kamzor hota jaata hai. Gravity bhi bilkul aise hi kaam karti hai, bas yeh har mass ke beech hoti hai, sirf magnets ke beech nahi.

Explanation

Newton ka Universal Law of Gravitation kehta hai ki universe mein har do objects ek doosre ko ek force se attract karte hain. Yeh force dono objects ke masses ke product ke proportional hoti hai, aur unke beech ki distance ke square ke inversely proportional hoti hai.

Mathematically: `F = G \frac{m_1 m_2}{r^2}`. Yahaan `F` gravitational force hai, `m_1` aur `m_2` dono objects ke masses hain, `r` unke centres ke beech ki distance hai, aur `G` universal gravitational constant hai jiska value `6.674 \times 10^{-11} \text{ N m}^2\text{/kg}^2` hai.

Is law ko 'universal' isliye kehte hain kyunki yeh HAR jagah apply hota hai — chahe do planets ke beech ho, tum aur dharti ke beech ho, ya do pencils ke beech. Bas chhoti objects ke beech yeh force itni tiny hoti hai ki feel nahi hoti.

Important properties: (1) Gravitational force hamesha ATTRACTIVE hoti hai — kabhi repulsive nahi. (2) Yeh ek action-reaction pair hai — Earth tujhe kheechti hai utni hi force se jitni tu Earth ko kheechta hai (Newton's third law). (3) Yeh force vacuum mein bhi kaam karti hai, kisi medium ki zaroorat nahi.

`G` ka value bohot chhota hai (`10^{-11}` order) — isliye do normal objects ke beech gravitational force negligible hoti hai. Lekin jab ek object bahut massive ho (jaise Earth, mass `\approx 6 \times 10^{24} \text{ kg}`), tab yeh force significant ban jaati hai aur cheezein girne lagti hain.

Worked example

Problem: Two objects of masses `1 \text{ kg}` and `2 \text{ kg}` are placed `1 \text{ m}` apart. Calculate the gravitational force between them. (`G = 6.674 \times 10^{-11} \text{ N m}^2\text{/kg}^2`)

1. Pehle diye gaye values note karo — `m_1`, `m_2` aur `r`.
2. Formula lagao — `F = G \frac{m_1 m_2}{r^2}`.
3. Calculate karo. Denominator `1` hai, toh sirf numerator solve karo.

Answer: `F = 1.33 \times 10^{-10} \text{ N}` (extremely small — isliye hum daily life mein do objects ke beech gravity feel nahi karte)

Problem: The mass of Earth is `6 \times 10^{24} \text{ kg}` and mass of Moon is `7.4 \times 10^{22} \text{ kg}`. The distance between them is `3.84 \times 10^8 \text{ m}`. Find the gravitational force between Earth and Moon.

1. Bahut bade numbers hain — carefully powers of `10` handle karo.
2. Formula mein values daalo.
3. Pehle numerator: `6.674 \times 6 \times 7.4 = 296.33`, powers: `10^{-11+24+22} = 10^{35}`.
4. Denominator: `(3.84)^2 = 14.75`, `(10^8)^2 = 10^{16}`.
5. Divide karo: `296.33/14.75 \approx 20.09`, `10^{35}/10^{16} = 10^{19}`.

Answer: `F \approx 2.01 \times 10^{20} \text{ N}` — yeh woh force hai jo Moon ko Earth ke orbit mein rakhti hai.

Key points

• The Law (statement): Every object attracts every other object with a force `F = G \frac{m_1 m_2}{r^2}`, where `G = 6.674 \times 10^{-11} \text{ N m}^2\text{/kg}^2`.
• Always attractive: Gravitational force is always attractive, never repulsive.
• Universal constant G: `G` is the same everywhere in the universe; it does not depend on the medium or the objects.
• Inverse-square law: If distance doubles, force becomes `1/4\text{th}`; if distance triples, force becomes `1/9\text{th}`.

Common mistakes

• r ko square karna bhoolna: Formula mein `r^2` hai, `r` nahi. Agar sirf `r` se divide karo toh answer bahut bada aa jaayega. Hamesha yaad rakho — inverse SQUARE law.
• G aur g confuse karna: `G` (capital) universal gravitational constant hai (`6.674 \times 10^{-11} \text{ N m}^2\text{/kg}^2`), jabki `g` (small) acceleration due to gravity hai (`9.8 \text{ m/s}^2`). Dono alag hain.

Recall questions

• State Newton's Universal Law of Gravitation.
• What is the value and SI unit of the universal gravitational constant `G`?
• If the distance between two objects is doubled, how does the gravitational force change?

Questions & answers

State the universal law of gravitation. What is the importance of the universal law of gravitation?

Every object attracts every other object with `F = G \frac{m_1 m_2}{r^2}`. Its importance: (1) it explains why objects fall to the ground, (2) it explains the motion of the Moon around the Earth, (3) it explains the motion of planets around the Sun, and (4) it explains tides caused by the Moon and the Sun.

Approach: State the law with formula, then list 3-4 phenomena it explains.

What happens to the gravitational force between two objects when their masses are doubled and the distance between them is also doubled?

`F' = G \frac{(2m_1)(2m_2)}{(2r)^2} = \frac{4 G m_1 m_2}{4 r^2} = G \frac{m_1 m_2}{r^2} = F`. The force remains the same.

Approach: Substitute `2m_1`, `2m_2`, `2r` into the formula and simplify.

Continue learning

Next: Apply F = G m1 m2 / r^2

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