Question

Derive the expression for universal law of gravitation​

Answer 1

Answer:

The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is F=GmMr2 F = G mM r 2 , where F is the magnitude of the gravitational force. G is the gravitational constant, given by G = 6.673 × 10−11 N·m2/kg2.

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Answer 2

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According to Newton's Law of Gravitation,

i) Gravitational Force is linearly proportional to product of masses.

$= > \mathrm{ F \propto \: Mm}............(1)$

and,

ii) Gravitational Force is inversely proportional to square of distance separating the objects' centre.

$= > \mathrm{ F \propto \frac{1}{ {R}^{2} } }............(2)$

Multiply (1) and (2),

$\mathrm{F \propto \frac{Mm}{ {R}^{2} } }$

$= > \mathrm{ F= \frac{GMm}{ {R}^{2} } }$

Hence, Universal law of Gravity is given by:

F = GMm/r^2.