Question

state universal law of gravitation and give its mathematical expression. ​

Answer 1

Answer:

The law of universal gravitation or the universal law of gravitation is related to the masses and the distance between any two bodies in the universe. It is directly proportional to the product of the masses between which it acts and the universal gravitational constant G. Formula used: F=Gm1m2r2.

Explanation:

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Answer 2

Answer:

➟ The gravitational force of earth is known as gravity i.e., gravity is the force by which earth pulls a body toward it's centre.

➟ Gravitation- Every body attract other body by a force called force of gravitation.

➣ Newton's law of gravitation- The force of gravitational attraction between two points bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Considering two points ${\sf{m_{1} \: and \: m_{2}}}$ are placed at a distance ${\sf{r}}$ The force of gravitational attraction between them, ${\sf{F \: = G\dfrac{m_{1}m_{2}}{r^{2}}}}$

Here ${\sf{G}}$ is constant called universal gravitational constant. The value of G is ${\sf{6.67 \times 10^{-11} Nm^{2}/kg^{2}}}$

Now let's derive!

↪️ Let two objects A and B of masses M and m lie at a distance, d from each other.

Now let the force of attraction between then be F.

↪️ Now according to the universal law of gravitation, the force between two objects is directly proportional to their masses. Therefore,

→ F ∝ M × m

→ F ∝ Mm – – – Equation 1

↪️ And we also know that the force between two objects is inversely proportional to the square of the distance between them. Therefore,

→ F ∝ 1/(d)² – – – Equation 2

↪️ From – – – Equation 1 and 2

→ F ∝ Mm/(d)²

Let's remove proportional sign, by adding constant as G here

→ F = GMm/(d)²

Henceforth,

→ G = Fd²/Mm Henceforth, derived!

Figure regards,

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Additional information:

➟ The acceleration produced in a body due to force of gravity is known as acceleration due to gravity. Acceleration due to gravity is denoted by “g”. And g's value is 9.8 m/s².

➣ Acceleration due to gravity is independent of shape, mass and size of the mass of the body.

g is the symbol for acceleration due to the gravity and G is the symbol of universal law of gravitation that is gravitational constant.

Difference between g and G for more knowledge about the both!

$\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|cc}\bf Gravitation &\bf Gravity\\\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}&\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}\\\sf It \: is \: that \: attracting \: force &\sf Force \: of \: gravity \: is \: gravitation \: pull \: on \: a \: body \\ \sf applied \: between \: any \: 2 \: bodies \: of \: universe &\sf \: near \: or \: on \\ &\sf \: the \: surface \: of \: the \: earth \\ \\ \sf It \: is \: a \: universal \: force & \sf It \: isn't \: a \: universal \: force \\ \\ \sf Gravitation \: is \: attracting \: force & \sf Gravity \: is \: a \: pulling \: force \\ \\ \sf Gravitation \: is \: a \: weak \: force & \sf It \: isn't \: weak \: as \: gravitation \\ \\ \sf G \: is \: symbol \: for \: gravitation & \sf g \: is \: symbol \: for \: gravity \\ \\ \sf G \: = \dfrac{Fd^2}{Mm} & \sf g \: = \dfrac{GM}{R^2} \end{array}} \end{gathered}\end{gathered}$