Question

state universal law of gravitation. derive the formula for the gravitational force using the factor on which it depends​

Answer 1

Statement :

• The gravitational force between two bodies will be equal to the mass product of the masses and inversely proportional to the square of the distance between them
• F = GMm/d²

Derivation :

☯ We know that if the mass of the body is more then the gravitational force is more, so then we may concluded that the gravitational force is directly proportional to the mass of the body

☯ Also we know that as the distance increase then the gravitational force decrease and hence we may here concluded that the gravitational force is inversely proportional to the distance between the bodies

━━━━━━━━━━━━━━━━━━━━━━━━━

✭ Conclutions :

⇒ G ∝ Mass

⇒ G ∝ 1/Distance

⇒ G ∝ Mm/d²

• So here to remove the proportional symbol we introduce a constant, i.e "G" (Universal Gravitational Constant)

⇒ F = GMm/d²

Hence Proved!!

Answer 2

$\mathbb{\color{indigo}UNIVERSAL\:LAW\:OF\:GRAVITATION\:;-}$

• It states that every particle in the universe attracts all other particle with a force which directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$\Large\bf\pink{DeRiVaTiOn\:;-}$

• See the attachment diagram for explanation.

✔ If $\bf\red{\mid\vec{F_{12}}\mid\:=\:\mid\vec{F_{21}}\mid\:=\:F\:}$

$\bf\blue{Then,}$

$:\implies\:\:\bf{F\:\propto\:m_1\:m_2\:\:\:\:\:\:\:\:\&\:\:\:\:\:\:\:\:F\:\propto\:\dfrac{1}{r^2}\:}$

$\bf\green{So,}$

$:\implies\:\:\bf{F\:\propto\:\dfrac{m_1m_2}{r^2}\:}$

$\therefore\:\:\bf\purple{F\:=\:\dfrac{Gm_1m_2}{r^2}\:}$

$\Large\bf\orange{Where,}$

• G = Universal gravitational constant.

[NoTe - This formula is applicable only for spherically symmetric masses or point masses.]

FACTORS DEPENDS ON "F" ;-

1. Inertia.
2. Expansion.