Question

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

Answer 1

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

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 -

$F \: \alpha \: ( \: m1 \: \times \: m2)$

and

$F \: \alpha \: \frac{1}{ {r}^{2} }$

Combining both equations , we get

$F \: \alpha \: \frac{m1 \times m2}{ {r}^{2} }$

$F\: = G \frac{m1 \times m2}{ {r}^{2} }$

where G is constant , known as universal gravitational constant.

Here , if m1 & m2 of two bodies are of 1 kg and the distance ( r ) between them is 1 m , then

The force of gravitation =

$F \: = \: G$

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.