Question

The value of universal gravitational constant on earth for a particle of mass 5 kgs is:
A. $$6.67\times {10}^{-11}$$
B. $$6.67\times {10}^{-7}$$
C. $$5\times 6.67\times {10}^{-11}$$
D. $$6.67\times {10}^{-23}$$

Answer 1

Hint: The universal gravitational constant is the proportionality constant used in Newton’s Law of Universal Gravitation. It is commonly denoted by G. It is different from g, which denotes the acceleration due to gravity.

Complete step by step answer:
According to Newton's law of universal gravitation, the force of gravitational attraction is given by,
$$F={\displaystyle \frac{G{m}_1{m}_2}{r^2}}$$
Where,
F = gravitational force of attraction
G = universal gravitational constant
$m_1$ = mass of an object
$m_2$ = mass of another object
r = distance between two objects
Which can be written as,
$$G={\displaystyle \frac{F{r}^2}{m_1{m}_2}}$$
The universal gravitational constant (G) relates the magnitude of the gravitational attraction force between two bodies to their masses and the distance between them. Its value is extremely difficult to measure experimentally.
Since the universal gravitational constant (G) is a universal constant and its value is independent of the masses or place wherever the masses are situated.
So, its value remains constant i.e., $$6.67\times {10}^{-11}N{m}^2/k{g}^2$$
Hence, the correct option is A, i.e., $$6.67\times {10}^{-11}$$

Additional Information:
The gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a relatively greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is also doubled.

Note: Students should understand Newton's Law of Universal Gravitation and thereafter they need to know how to define the universal gravitational constant (G). Students should also keep in mind that its value remains unchanged with various ranges of masses, distances and places. Students do not need to confuse between G (universal gravitational constant) and g (acceleration due to gravity).