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

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 $g{\text{ }} = \sqrt {\dfrac{{GM}}{{{r^2}}}}$