Question

State Newton's law of gravitation. Give its mathematical expression​.​

Answer 1

Newton's Law of Gravitation :-

Every body in the universe attract every others body with a force which is directly proportional to the product of thier masses and inversely proportional to the square of the distance between them.

Note: law of gravitation also known as universal law of gravitation.

Let us consider two objects of mass "m₁" and "m₂" at a distance r and the force of attraction between the two objects be F.

$: \implies \sf{F \propto m_{1} \times m_{2} \: ..(i)}$

$: \implies \sf{F \propto \dfrac{1}{ {r}^{2} } \: ..(ii)}$

From equation (i) and (ii)

${: \implies \sf{F \propto \dfrac{ m_{1} \times m_{2} }{ {r}^{2} } }}$

${: \implies \sf{F = G \times \dfrac{ m_{1} \times m_{2} }{ {r}^{2} } }}$

Where, G is constant and also known an universal gravitational constant.

${ \underline { \boxed {: \implies \sf{F = G \times \dfrac{ m_{1} \times m_{2} }{ {r}^{2} } }}}} \: \red\bigstar$

Thanks!

Answer 2

$\bf\huge\underline{Answer:-}$

Newton's universal law of gravitation: Every object in the Universe attracts every other object with a definite force. This force is directly proportional to the product of the masses of the two object s and inversely proportional to the square of the distance between them.

Mathematical form : Consider two objects of masses m1 and m2. We assume that the objects are very small spheres of uniform density and the distance r between their centres is very large compared to the radii of the spheres.

The magnitude (F) of the gravitational force of attraction between the objects is directly proportional to m1m2 and inversely proportional to r2.∴

where G is the constant of proportionally , called the universal gravitational constant .

:)