Question

Question :-

➠ Derive expression for force of attraction between two bodies and then define gravitational constant.

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Answer 1

Answer:

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Explanation:

“Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” Let us consider two bodies A and B of masses m1 and m2 which are separated by a distance r. Then the force of gravitation (F) acting on the two bodies is given by

$F ∝ m _1 \times m_2 \: \: - - - (1) \\ \\ and \: F ∝ \frac{1}{ {r}^{2} } \: \: - - - (2) \\ \\ conbining \: (1) \: \: and \: \: (2) \\ \\ F ∝ \frac{m _1 \times m_2}{{r}^{2}} \\ \\F = G \times \frac{m _1 m_2}{ {r}^{2} } \: \: - - - (3)$

where G is constant known as universal gravitational constant

Here the masses M1 and M2 of the two bodies are of 1 kg and the distance are between them is 1 m

Then putting m1 = 1 kg, m2 = 1 kg and r = 1m in equation (3),we will get

G = F

Thus, the gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other.

Answer 2

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$\huge\bf{Answer:-}$

Universal Law of Gravitation : It states that the force of attraction between two

bodies is directly proportional to the

product of their masses and inversely proportional to the square of the

distance

between them.

Let the two bodies 'A' and 'B' be of masses 'M' and 'm' respectively,

which are separated by a distance According

to Universal Law of Gravitation,

F = GM × m²

Where, 'G' is called universal gravitation constant.

The numerical value of G

$= 6.65 \times 10 {}^{ - 11}Nm {}^{2} kg {}^{2}$

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