Question

On which of the following factors does the value of gravitational constant (G) depend?
${\text{A}}{\text{.}}$ The nature of the interacting bodies
${\text{B}}{\text{.}}$ The size of the interacting bodies
${\text{C}}{\text{.}}$ The mass of the interacting bodies
${\text{D}}{\text{.}}$ None of these

Answer 1

Hint: Here, we will proceed by defining the gravitational force of attraction. Then, we will state Newton's universal law of gravitation. Finally, we will obtain the expression for gravitational force of attraction.

Complete answer:
Gravitational force is a force that draws mass to every two objects. We consider attractive gravitational force because it always tries to pull masses together, it never drives them apart. In fact, every object is pulling on every other object in the whole universe, including you! That is called the universal law of gravitation by Newton. Of course, you don't have a very large mass and so, you don't pull much on those other objects. And objects really far apart from each other also don't noticeably pull on each other. But there is the force, and we can compute it.
The Law of Universal Gravitation states that each point mass attracts any other point mass in the universe by a force pointing in a straight line towards the center of mass of both points, and this force is proportional to the masses of the objects, and inversely proportional to their separation. The Law refers to all massed objects, large or small.
If two bodies have masses M and m divided by a distance r, then the gravitational force of attraction is given by
${\text{F}} \propto {\text{Mm}}$ and ${\text{F}} \propto \dfrac{1}{{{{\text{r}}^2}}}$
By combining the above inequalities, we have
 ${\text{F}} \propto \dfrac{{{\text{Mm}}}}{{{{\text{r}}^2}}}$
By eliminating the proportionality sign and using a constant G, we get
${\text{F}} = \dfrac{{{\text{GMm}}}}{{{{\text{r}}^2}}}$ where F denotes the gravitational force of attraction, G denotes the gravitational constant, M denotes the mass of one object, m denotes the mass of the other object and r denotes the distance of separation between these two objects.
Clearly, we can see that the gravitational constant (G) is a constant and its value is equal to 6.674$ \times {10^{ - 11}}{\text{ }}\dfrac{{{\text{N}}{{\text{m}}^2}}}{{{\text{k}}{{\text{g}}^2}}}$ and doesn’t depend on any factor.

So, the correct answer is “Option D”.

Note:
Two large objects may be known as point-like masses if there is a very large distance between them relative to their sizes or if they are spherically symmetrical. The mass of each object can be represented as a point mass at its center of mass for these cases.