HP TGT Non-Medical exam mein Gravitation ek aisa chapter hai jahan se conceptual aur numerical dono tarah ke sawal aate hain. Kya aap jante hain ki Moon par humara wazan (weight) kam kyun ho jata hai? Ya Rocket ko space mein bhejne ke liye kitni speed chahiye?
Aaj hum Newton ke Universal Law se lekar Kepler ke Grah Gati Niyam tak sab kuch cover karenge.
1. Universal Law of Gravitation (Gurutvakarshan ka Niyam)
Newton ke anusar, brahmand (universe) ki har vastu doosri vastu ko apni taraf khinchti hai.
Formula:
$$F = G \frac{m_1 m_2}{r^2}$$Universal Gravitational Constant ($G$):
Value:
$6.67 \times 10^{-11} \text{ Nm}^2/\text{kg}^2$ Note: Yeh poore universe mein kahin nahi badalta (Isliye ise 'Universal' kehte hain).
2. Acceleration Due to Gravity ($g$) - Most Important
Prithvi jis acceleration se cheezon ko apni taraf khinchti hai.
Formula:
$$g = \frac{GM}{R^2}$$(Jahan $M$ = Mass of Earth, $R$ = Radius of Earth).
Standard Value:
$9.8 \text{ m/s}^2$ (Numericals mein $10$ le sakte hain).
Variation of 'g' (Exam Special):
'g' ki value har jagah same nahi hoti:
Height (
$h$): Prithvi ki satah se upar jane par 'g' ghat-ta (decreases) hai. Depth ($d$): Khadan (mine) mein niche jane par bhi 'g' ghat-ta hai.
Center of Earth: Prithvi ke kendra par 'g' Zero ($0$) hota hai.
Shape of Earth:
Poles (Dhruv): Radius kam hai, isliye 'g' Maximum hota hai.
Equator (Bhumadhya Rekha): Radius zyada hai, isliye 'g' Minimum hota hai.
Exam Trick: Agar koi vyakti Equator se Pole ki taraf jaye, toh uska Weight badhega.
3. Kepler’s Laws of Planetary Motion (Grah Gati ke Niyam)
Planets Sun ke chaaron taraf kaise ghoomte hain, yeh Kepler ne bataya.
Law of Orbits: Sabhi planets Sun ke chaaron taraf Elliptical (Andakar) orbit mein ghoomte hain, aur Sun ek focus par hota hai.
Law of Areas: Planet ki Areal Velocity constant hoti hai.
Meaning: Jab Planet Sun ke paas hota hai, toh tez chalta hai; door hota hai toh dheere.
Law of Periods: Time period (
$T$) ka square, distance ( $R$) ke cube ke proportional hota hai. $$T^2 \propto R^3$$
4. Mass vs Weight (Dravyaman vs Bhaar)
Yeh confusion door kar lein:
| Property | Mass (m) | Weight (W) |
| Definition | Amount of matter. | Force of gravity ($W=mg$). |
| Quantity | Scalar. | Vector. |
| Variation | Constant everywhere. | Changes with 'g'. |
| Unit | Kilogram (kg). | Newton (N). |
| At Center | Same rahega. | Zero ho jayega. |
Fact: Moon par gravity Earth ki
$1/6$ hai. Isliye wahan Weight bhi $1/6$ hoga.
5. Escape Velocity ($v_e$) (Palayan Veg)
Woh minimum speed jo kisi cheez ko Earth ki gravity se bahar fenkne ke liye chahiye.
Formula:
$$v_e = \sqrt{2gR}$$Value for Earth: $11.2 \text{ km/s}$.
Note: Yeh object ke mass ($m$) par depend nahi karti. Haathi aur cheenti dono ke liye escape velocity same hogi.
6. Satellites (Upagrah)
Orbital Velocity ($v_o$): Orbit mein ghoomne ke liye speed.
$$v_o = \sqrt{gR} \approx 8 \text{ km/s}$$Relation: $v_e = \sqrt{2} v_o$
Geostationary Satellite (Bhu-sthir):
Yeh Earth ke saath-saath ghoomta hai.
Height: $36,000 \text{ km}$.
Time Period: $24 \text{ Hours}$.
7. Important Formulas Table
| Concept | Formula |
| Gravitational Force | $F = G \frac{m_1 m_2}{r^2}$ |
| Gravity ($g$) | $g = \frac{GM}{R^2}$ |
| Kepler's 3rd Law | $T^2 \propto R^3$ |
| Escape Velocity | $v_e = \sqrt{2gR}$ |
| Weight | $W = mg$ |
8. HP TGT Special MCQs (Exam Level)
Q1. The value of 'g' is maximum at:
A) Equator
B) Poles
C) Center of Earth
D) Mount Everest
Ans: B (Poles par radius sabse kam hoti hai).
Q2. If the distance between two masses is doubled, the gravitational force becomes:
A) Double
B) Four times
C) One-fourth ($1/4$)
D) Half
Ans: C (Formula: $F \propto 1/r^2$. So, $1/(2)^2 = 1/4$).
Q3. Escape velocity from Earth depends on:
A) Mass of the object
B) Mass of Earth
C) Direction of projection
D) None
Ans: B (Object ke mass par depend nahi karti).
Q4. Weight of a body at the center of Earth is:
A) Infinite
B) Zero
C) Same as surface
D) None
Ans: B (Kyunki $g=0$ at center).
Q5. Kepler’s second law (Law of Areas) is based on conservation of:
A) Energy
B) Linear Momentum
C) Angular Momentum
D) Mass
Ans: C (TGT Favorite Question).
8. Gravitational Potential Energy (Gurutviya Sthitij Urja)
Humne padha hai ki $P.E. = mgh$, lekin space mein jahan 'g' badalta hai, wahan formula alag hota hai.
Formula:
$$U = -\frac{GMm}{r}$$Negative Sign ka matlab:
Negative sign yeh darshata hai ki Gurutvakarshan ek Attractive Force hai. Agar humein kisi cheez ko Earth se door le jana hai, toh humein work karna padega (Energy deni padegi).
Binding Energy: Satellite ko orbit mein banaye rakhne ke liye jo energy chahiye, wo Binding Energy kehlati hai.
9. Weightlessness (Bhaar-hinta) - Conceptual
Aksar log sochte hain ki space mein gravity nahi hoti, isliye weight zero hota hai. Yeh galat hai.
Reason: Weight humein tab mehsoos hota hai jab zameen hum par wapas force (Reaction Force) lagati hai.
In Satellite: Satellite free fall ki sthiti mein hoti hai (lagatar Earth ki taraf gir rahi hoti hai). Isliye Reaction Force ($R$) = 0 ho jata hai.
Result: Astronaut ko apna wazan zero lagta hai, bhale hi wahan gravity मौजूद ho.
Artificial Gravity: Space station ko ghoomakar (rotate karke) nakli gravity paida ki ja sakti hai.
10. Tides (Jwar-Bhata)
Samundar mein paani ka uthna aur girna (Tides) bhi Gravitation ka nateeja hai.
Cause: Moon (Chandrama) aur Sun ka gravitational pull.
Moon is Stronger: Bhale hi Sun bada hai, lekin Moon Earth ke zyada paas hai, isliye Tides par Moon ka asar zyada hota hai ($2/3$rd effect).
11. Difference between 'G' and 'g' (Exam Favorite)
Yeh table yaad kar lein, aksar matching questions aate hain:
| Feature | Universal Constant (G) | Acceleration due to Gravity (g) |
| Meaning | Force between unit masses. | Acceleration due to Earth. |
| Value | $6.67 \times 10^{-11}$ | $9.8 \text{ m/s}^2$ |
| Nature | Scalar (Adish). | Vector (Sadish). |
| Variation | Constant everywhere. | Places ke hisab se badalta hai. |
| Unit | $\text{Nm}^2/\text{kg}^2$ | $\text{m/s}^2$ |
12. Advanced Numericals (Mains Level)
TGT Commission mein numericals thode tricky aate hain.
Problem 1 (Force Calculation):
Two objects of mass $10 \text{ kg}$ and $20 \text{ kg}$ are kept $5 \text{ m}$ apart. Calculate Gravitational Force. ($G = 6.7 \times 10^{-11}$)
Solution:
$F = G \frac{m_1 m_2}{r^2}$
$F = \frac{6.7 \times 10^{-11} \times 10 \times 20}{(5)^2}$
$F = \frac{6.7 \times 10^{-11} \times 200}{25} = 53.6 \times 10^{-11} \text{ N}$.
Conclusion: Yeh force bohot kam hai, isliye humein mehsoos nahi hota.
Problem 2 (Percentage Change):
Agar Earth ka radius $1\%$ sikud (shrink) jaye (Mass same rahe), toh 'g' par kya asar padega?
Trick: $g \propto \frac{1}{R^2}$.
Agar $R$ ghatega, toh $g$ badhega.
Change $\approx 2 \times (\% \text{ change in } R) = 2 \times 1\% = 2\%$.
Answer: 'g' ki value $2\%$ badh jayegi.
13. Black Hole (Krishna Vivar) - Extra Knowledge
Jab kisi star ka mass bohot zyada ho aur wo apne hi gravity mein dhans jaye, toh wo Black Hole ban jata hai.
Escape Velocity: Black hole ki escape velocity Light ki speed ($c$) se bhi zyada hoti hai. Isliye wahan se roshni bhi bahar nahi aa sakti.
Conclusion
Gravitation chapter mein Variation of 'g' aur Satellite ke questions sabse zyada important hain. Yaad rakhein ki $G$ (constant) aur $g$ (variable) mein zameen-aasmaan ka fark hai.
Next Chapter:
Agli post mein hum "Sound & Waves" (Dhwani aur Tarang) padhenge. Hum samjhenge ki Chandrama par hum ek doosre ki awaz kyun nahi sun sakte?
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