Newton's law of gravitation — universal, action at distance: Question bank

1.2.19 · D5 · Physics › Newton's Laws & Dynamics › Newton's law of gravitation — universal, action at distance

Yeh pure-reasoning items hain. Calculators nahi — agar numbers plug karne ki urge ho, toh woh item computation pages pe belong karta hai, yahan nahi.

Pehle — characters ki cast (trap se pehle define karo)

Ek symbol jise tum jaante nahi, usme trap nahi pakad sakte. Toh yahan is page pe use hone wale har symbol ko, plain words mein, kisi bhi question se pehle diya gaya hai.

Figure — Newton's law of gravitation — universal, action at distance

Figure mein do red force arrows same length ke hain lekin opposite directions mein point karte hain — yeh gravity mein built-in Newton's Third Law hai, aur yeh woh visual hai jo "product vs sum" question padhte waqt tumhare dimag mein rehni chahiye.

True ya false — justify karo

True ya false: Agar dono masses double karo, toh gravitational force double ho jaati hai.

False — force

\propto m_{1} m_{2}

(product), toh har ek ko double karne se product

2 \times 2 = 4

se multiply hota hai. Force chaar guna hoti hai, double nahi.

True ya false: Earth, Moon ko Moon se zyada zor se kheenchti hai.

False — upar figure mein dono red arrows barabar length ke hain:

F_{12} = F_{21}

by Newton's Third Law. Moon sirf zyada accelerate nahi karta kyunki usse shift karna zyada mushkil hai; jo force usse milti hai woh same hoti hai.

True ya false: Do objects ke beech gravity ko beech mein shield rakhke band kiya ja sakta hai.

False — koi "anti-gravity" material abhi tak nahi mila. Electric charge ke unlike, mass sirf ek sign mein aata hai (hamesha attract karta hai), isliye koi cheez field ko cancel nahi kar sakti jaise conductor electric field ko cancel karta hai.

True ya false: Moon pe giraaye gaye ek pankh aur ek hammer saath zameen pe girate hain.

True — object ki apni mass cancel ho jaati hai (dekho "Why questions" mein worked cancellation), bacha sirf

a = GM / r^{2}

, jisme girne wale object ka koi reference nahi. Moon pe hawa nahi hai, toh dono same

g_{Moon}

se girate hain.

True ya false: Agar distance

r

teen guna ho jaaye, toh force ek-tihaayi reh jaati hai.

False — yeh inverse-square hai (denominator mein

r^{2}

), toh force

1/ 3^{2} = 1/9

reh jaati hai. Distance teen guna karne se pull naau guna weak ho jaati hai; end mein figure mein falloff curve dekho.

True ya false: Constant

G

Jupiter pe zyada bada hota hai kyunki Jupiter ki gravity zyada strong hai.

False —

G

universal hai, poore cosmos mein identical. Jupiter strong lagta hai kyunki uska

g = GM / r^{2}

bada hai (bahut bada

M

);

G

khud kabhi nahi badalta.

True ya false: Earth ke exact centre pe tumhe enormous gravitational pull feel hogi.

False — centre pe, mass har direction se barabar gherta hai aur har pull cancel ho jaati hai, toh net gravity zero hai (neeche shell-cancellation figure dekho).

True ya false: Kyunki gravity "action at a distance" hai, yeh distant stars tak instantly pahunchti hai.

Reality mein False — Newton ke model ne instant action assume kiya tha, lekin General Relativity dikhata hai ki gravitational influence light ki speed

c

se travel karta hai, infinitely fast nahi.

True ya false: Weight aur mass ek hi quantity ke do naam hain.

False — mass (

m

, kg mein) matter ki matra hai aur kabhi nahi badlata; weight us par force

W = m g

hai (newtons mein), jo Moon pe kam ho jaata hai kyunki wahan

g

chhota hai. Dekho Weight vs Mass.

Error pakdo

Error pakdo: "

F = GM m / r^{2}

mein Earth pe khade ek insaan ke liye,

r

insaan ki zameen se upar height hai, toh

r \approx 1.7

m."

Galat — hamare definition ke anusaar,

r

centre-to-centre distance hai, toh

r = R_{\oplus} \approx 6.37 \times 1 0^{6}

m hai, surface height nahi. Poora sphere aise pull karta hai jaise uski saari mass uske centre pe ho (yeh Shell Theorem hai, neeche draw kiya gaya hai).

Error pakdo: "Kyunki

F

dono masses par depend karta hai, ek bhaari ball ek halki ball se zyada tez girti hai."

Force bhaari ball ke liye zyada hoti hai, lekin uski inertia bhi zyada hoti hai. Force ko mass se divide karo,

a = F / m = GM / r^{2}

— object ki mass cancel ho jaati hai, toh dono same acceleration se girte hain.

Error pakdo: "

g

aur

G

dono gravity constants hain jinka value lagbhag

9.8

hai."

Sirf

g \approx 9.8 m/s^{2}

Earth ki surface ke paas, aur yeh local hai (planet aur altitude ke saath badlata hai).

G = 6.674 \times 1 0^{- 11} N m^{2} k g^{- 2}

ek universal constant hai bilkul alag units ke saath.

Error pakdo: "Astronauts ISS pe float karte hain kyunki wahan upar gravity nahi hoti."

Us altitude par kaafi gravity hai (surface value ka roughly 90%). Woh float karte hain kyunki woh continuous free fall mein hain: neeche free-body figure dikhata hai ki gravity act karti hai lekin koi floor push back nahi karta, toh koi normal force nahi — station aur astronaut saath Earth ke around girate rehte hain.

Error pakdo: "Formula

F_{12} = + \frac{G m _{1} m _{2}}{r ^{2}} \overset{r}{^}_{12}

use karta hai jahan

\overset{r}{^}_{12}

2 se 1 ki taraf point karta hai."

Upar define kiya gaya hai,

\overset{r}{^}_{12}

1 se 2 ki taraf point karta hai (blue arrow).

+

sign attraction encode karta hai sirf us convention ke saath; agar arrow ki direction flip karo toh sign bhi flip karna padega, warna force galat direction mein point karegi.

Error pakdo: "Distance double karna aur ek mass double karna force ko unchanged chhod deta hai."

Ek mass double karne se

F

mein

2

ka multiplication hota hai; distance double karne se

F

mein

2^{2} = 4

ka division hota hai. Net effect

2/4 = 1/2

hai, toh force half hoti hai, unchanged nahi.

Why questions

Force product

m_{1} m_{2}

par kyun depend karta hai na ki sum

m_{1} + m_{2}

par?

m_{1} m_{2}

aur

m_{1} + m_{2}

dono symmetric hain, toh symmetry akele decide nahi kar sakti. Deciding argument physical hai: har object chote bits se bana hai, aur

m_{1}

ka har bit

m_{2}

ke har bit ko kheenchta hai — yeh ek multiplication hai (

m_{1}

bits

\times

m_{2}

bits), product deta hai. Sum galat predict karta ki jab ek mass zero ho tab bhi nonzero force hogi.

Gravity inverse-square kyun hai aur inverse-distance kyun nahi?

Ek point source ka influence ek expanding sphere ki surface par failta hai jiska area

4 π r^{2}

hai. Wahi total influence area

\propto r^{2}

par dilute hone se intensity

1/ r^{2}

se fall karti hai — same geometry jaise light aur sound.

Do everyday objects ke beech gravitational pull hum kyun barely feel karte hain?

G

bahut minuscule hai (

\sim 1 0^{- 11}

), toh ordinary masses ke beech force ek bacteria ke weight se bhi choti hoti hai. Hum gravity tabhi notice karte hain jab ek mass astronomically bada ho, jaise poori Earth.

"Falling Moon" calculation ne Newton ko kyun convince kiya ki gravity universal hai?

Moon ka orbital (centripetal) acceleration exactly surface

g

1/6 0^{2}

se scale hone par match kiya (kyunki Moon

\approx 60

Earth-radii door hai). Same law, same number — proof ki apple-force aur Moon-force ek hi hain. Dekho Kepler's Laws.

Gravitational field

g

introduce karne se "action at a distance" ki chinta kyun kam hoti hai?

Do masses empty space ke paar ek doosre ko pakadne ki jagah, har mass apne aas-paas ke space ko ek field se bharta hai, aur koi bhi doosra mass sirf apni jagah pe field ko respond karta hai — interaction spooky-at-a-distance ki jagah local ho jaata hai. Dekho Gravitational Field & Potential.

Earth ke paas free fall mein object ki apni mass uski acceleration mein kyun nahi aati?

Do facts side by side likho: gravity deta hai

F = G M_{\oplus} m / R_{\oplus}^{2}

, aur Newton's second law deta hai

F = ma

. Inhe equal karo:

ma = G M_{\oplus} m / R_{\oplus}^{2}

. Girne wala mass

m

dono sides pe hai, toh divide kar do:

a = G M_{\oplus} / R_{\oplus}^{2} = g

m

ke baare mein kuch nahi bachta — exactly isliye Galileo ne dekha ki saare objects saath girte hain.

Edge cases

Edge case: Jab do point masses same location par hon,

r = 0

, toh gravitational force kya hogi?

Formula deta hai

F = G m_{1} m_{2} /0

, jo infinity tak diverge karta hai — sign hai ki point-mass idealisation wahan breakdown karti hai. Real extended bodies ki mass failti hoti hai, toh yeh singularity physically kabhi nahi hoti (sirf black holes ki theory mein).

Edge case: Do masses

1 0^{10}

light-years door hain. Kya force exactly zero hai?

Nahi — inverse-square ka matlab hai force zero ki taraf shrink karti hai lekin kisi bhi finite distance par exactly zero kabhi nahi hoti. Har bit of matter har doosre bit ko kheenchta hai; "universal" ka yehi matlab hai.

Edge case: Do masses mein se ek zero hai (empty space, koi test particle nahi). Kaunsi force act karti hai?

Zero —

m_{2} = 0

ke saath product

m_{1} m_{2} = 0

. Field

g = GM / r^{2}

space mein abhi bhi exist karta hai, lekin kuch nahi hai wahan jo usse sample kare, toh koi force nahi. Dekho Gravitational Field & Potential.

Edge case: Tum ek uniform hollow spherical shell ke andar ho. Shell se tumhe kya gravity feel hogi?

Har jagah andar exactly zero, kisi bhi position par, sirf centre pe nahi. Neeche shell-cancellation figure dikhata hai kyun: paas wali wall zyada zor se kheenchti hai lekin mass ka chhota patch cover karti hai, jabki door wali wall kam zor se kheenchti hai lekin proportionally zyada mass cover karti hai — dono contributions exactly cancel ho jaate hain (Shell Theorem).

Edge case: Jaise tum Earth ke centre ki taraf ek mineshaft mein jaate ho, kya

g

badhta rehta hai?

Nahi — sirf tumhari current radius ke neeche ki mass tumhe pull karti hai (upar wala shell kuch contribute nahi karta). Tumhare neeche kam mass hone se,

g

depth ke saath actually decrease karta hai, centre par zero ho jaata hai. Iske ulat upar jaane se

g

1/ r^{2}

se girti hai — dono trends final figure mein draw hain.

Edge case: Kya Newton ka law Mercury ki orbit ke liye exact hai?

Lagbhag, lekin perfectly nahi — Mercury ki orbit Newton ke predict kiye se thoda zyada precess karti hai. Yeh chhoti discrepancy General Relativity explain karta hai, dikhata hai ki Newton ka law ek excellent approximation hai, final word nahi.

Shell results lock karne ke liye do pictures

Shell theorem upar teen alag traps mein invoke hota hai (Earth ka centre, hollow shell ke andar, mineshaft). Yahan cancellation ek baar draw kiya gaya hai, plus $g$ actually kaise vary karta hai jab tum andar aur bahar jaate ho — un items ko dobara padhte waqt yeh images dimag mein rakho.

Connections

Newton's Third Law — figure 1 mein equal-and-opposite red arrows.
Shell Theorem — centre-to-centre, hollow-shell, aur mineshaft items ko power deta hai.
Gravitational Field & Potential — action-at-a-distance ka field cure.
Circular Motion & Centripetal Force — free-fall / orbiting astronauts.
Kepler's Laws — falling-Moon universality check.
General Relativity — Mercury precession, finite-speed gravity.
Weight vs Mass — mass-vs-weight trap.