Question

12. Define universal law of gravitation write formula and diagram?



​

Answer 1

❒ The magnitude of gravitational force between two point masses is directly proportional to the product of masses and inversely proportional to the square of the distance between them.

This is known as Newton's law of gravitation also known as inverse square law.

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

Putting proportionality constant;

$:\implies\:\underline{\boxed{\bf{\red{F=G\:\dfrac{m_1m_2}{r^2}}}}}$

» F denotes force

» G denotes gravitational constant

» m₁ and m₂ denotes masses

» r denotes distance

SI unit of force : N (newton)

➤ Gravitational force is always attractive in nature.

➤ The law of gravitation is strictly true for point masses.

• For two bodies at any size provided they both have spherical symmetry.
• When one body has spherical symmetry and the other is small compared with the separation between their centres.
• When neither body has spherical symmetry but both are small compared with the separation between their centres.

➤ The value of G does not depend on the nature and size of the masses.

• G = 6.626 × 10‾¹¹ N m² / kg²

➤ The law of gravitation is universally valid. It applies to small objects on the earth, planets in the solar system and to galaxies.

Diagram :

$\setlength{\unitlength}{7mm} \begin{picture}(6,6)\thicklines\put(2,2){\circle{14}}\put(8,2){\circle{14}} \put(2,2){\circle*{0.15}} \put(8,2){\circle*{0.15}} \put(2,2){\line(1,0){6}} \put(4,2){\line( - 1,1){0.5}} \put(6,2){\line(1,1){0.5}} \put(4,2){\line( - 1, - 1){0.5}} \put(6,2){\line( 1, -1){0.5}} \put(4.5,0.7){\vector( - 1,0){2.7}} \put(5.4,0.7){\vector(1,0){2.8}}\put(4.75,0.6){ \bf r }\put( 3.3, - 1){ \framebox{ \bf F = \displaystyle \dfrac{G m_1m_2}{r^2} }}\put(1.6,3.5){ \bf m_1 }\put(7.6,3.4){ \bf m_2 }\end{picture}$

Answer 2

Answer:

Universal law of gravitation is proposed by great scientist "Sir Isaac Newton". It states that a body is attracted by other bodies in the universe i.e gravitation is directly proportional to the masses of the bodies and which is inversely proportional to the distance from the centre of those bodies.

Mathematically:

F = G Mm

d^2

M m

〇----------d------------〇

G is the universal gravitational constant

which is equivalent to 6.67×10^-11 m^3/kgs^2.

hope it helps