Question

$\huge\boxed{\mathtt\red{Question\::-}}$
Class :- 10 (ICSE)
Subject :- Physics
Derive the formula :-
$\large\boxed{\mathtt{F=G•\frac{m₁.m₂}{d²}}}$
From :-
• F = ma
• F ∝ m₁.m₂
• F ∝ 1/d²
Explain your derivation with examples.


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Answer 1

Explanation:

Well there is no derivation of this formula . It's no mathematical equation it's just basic principle to describe properties of objects that has mass .

It goes as follows that gravitational force F between two objects of mass m1 and M2 which are distance d apart is

$F \propto \: m_{1}m _2$

and

$F \propto \frac{1}{ { d}^{2} }$

By combining these to equation we get

$F \propto \frac{m_1m _2}{ {d}^{2} }$

When we remove the proptional sign there comes a constant G which is called gravitational constant

$F = G\frac{m_1m _2}{ {d}^{2} }$

Value of G is

$= 6.674 \times {10}^{ - 11} N {m}^{2} {(kg)}^{ - 2}$

Answer 2

Need to derive:

F= $\frac{GM1M2}{r^{2} }$

Solution:-

Let M1 be mass of particle 1

M2 be mass of particle 2

R be the distance between the two given particles

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

So,

F ∝ M1. M2 ----- i

Also

F∝$\frac{1}{r^{2} }$ ----- ii

Combining i and ii we get,

F∝$\frac{M1M2}{r^{2} }$

For removing the proportionality symbol, we must insert a constant. According to Newton the constant is G and it's value is 6.67 × 10−11 newton-metre2-kilogram−2.

Hence we get,

$\bold{\red{\boxed{F=G\dfrac{M1M2}{r^{2}}}}$