Question

In Newton’s gravitational law, \[F\, = \,\dfrac{{GmM}}{{{r^2}}}\] , the quantity G is:
(A) Depends on the value of g at the place of observation
(B) Is used only when one of the masses is earth
(C) Is greatest at the surface of the earth
(D) Is a universal constant in nature

Answer 1

Hint: G is known as universal gravitational constant. It has been observationally verified over two centuries in almost every real situation possible. It is invariant throughout the Universe.

Complete step by step solution:
Newton using his experiments devised that the force of gravitational between 2 distant objects will be directly proportional to the product of the masses of the 2 bodies.
 \[F \propto mM\]
Where m and M are the masses of the 2 bodies.
He further concluded that the force will be inversely proportional to the square of the distance between them. This is also known as the inverse square law.
 \[F \propto \dfrac{1}{{{r^2}}}\]
Combining these 2 relations, we get:
 \[F\, \propto \,\dfrac{{mM}}{{{r^2}}}\]
To the proportionality sign a constant was introduced,
 \[F\, = \,\dfrac{{GmM}}{{{r^2}}}\]
Where G is known as universal gravitational constant. Its value is given \[6.67 \times {10^ - }^{11}\;N{m^2}k{g^ - }^2\]. It has been almost 300 years since Newton and the value of G has been found constant throughout the Universe. This value will remain constant whatever may be the surrounding conditions.

Therefore the option with the correct answer is option D.
Note: G (gravitational constant) should not be confused with g( acceleration due to gravity). The relation between these 2 quantities is given as \[g{\text{ }} = \sqrt {\dfrac{{GM}}{{{r^2}}}} \]