Question
Derive an expression for the force of attraction between two bodies and then define gravitational constant.
✓
Answer
Newton's Law of universal gravitation: Everybody 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 $m_1$ and $m_2$ which are separated by a distance $d$.
Then the force of gravitation $(F)$ acting on the two bodies is given by
$F \propto m_1 \times m_2 ......(1)$
and $F \propto \frac{1}{d^2}......(2)$
Combining equations $(1)$ and $(2),$ we get
$F \propto \frac{m_1 \times m_2}{d^2}$
$F=k \frac{m_1 \times m_2}{d^2}$
Where, $k =$ proportionality constant, known as universal gravitational constant, $G$ having value $=6.67 \times 10^{-11} Nm ^2 \ kg^{-2}$.
Therefore, $F = G \times \frac{m_1 m_2}{d^2}$,
which is required expression for force of attraction between two bodies.
Here,
if the masses $m_1$ and $m_2$ of the two bodies are of $1 \ kg$ and the distance $( d )$ between them is $1 m$ ,
then putting $m _1=1 \ kg, m _2$
$=1 \ kg$ and $d =1 m$ in the above formula, we get
$F=G \times \frac{1}{1^2},$
$G=F$
Definition of the gravitational constant $G:$ 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.
Let us consider two bodies $A$ and $B$ of masses $m_1$ and $m_2$ which are separated by a distance $d$.
Then the force of gravitation $(F)$ acting on the two bodies is given by
$F \propto m_1 \times m_2 ......(1)$
and $F \propto \frac{1}{d^2}......(2)$
Combining equations $(1)$ and $(2),$ we get
$F \propto \frac{m_1 \times m_2}{d^2}$
$F=k \frac{m_1 \times m_2}{d^2}$
Where, $k =$ proportionality constant, known as universal gravitational constant, $G$ having value $=6.67 \times 10^{-11} Nm ^2 \ kg^{-2}$.
Therefore, $F = G \times \frac{m_1 m_2}{d^2}$,
which is required expression for force of attraction between two bodies.
Here,
if the masses $m_1$ and $m_2$ of the two bodies are of $1 \ kg$ and the distance $( d )$ between them is $1 m$ ,
then putting $m _1=1 \ kg, m _2$
$=1 \ kg$ and $d =1 m$ in the above formula, we get
$F=G \times \frac{1}{1^2},$
$G=F$
Definition of the gravitational constant $G:$ 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.
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