Question

The force of gravitation between two bodies can be zero if the separation between the bodies becomes
A. 1
B. 0
C. -1
D. infinity

Answer 1

Hint: The force of gravitation between two bodies can be described by Newton’s universal gravitation law. This law states that the gravitational force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.

Formula used: In this solution we will be using the following formulae;
\[F = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}\] where \[F\] is the gravitational force of attraction between two bodies, \[{m_1}\] is the mass of one and \[{m_2}\] is the mass of the other, \[r\] is the distance between them.

Complete step by step answer:
To know how the distance between the objects affects the gravitational force of attraction, we need to know the relationship between them.
Generally, according to Newton’s law, the force of attraction is directly proportional to the product of their masses and inversely proportional to the square of their distance apart. Or more accurately, the length of the line joining the centres of the two bodies.
The force can be mathematically given by
\[F = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}\] where \[F\] is the gravitational force of attraction between two bodies, \[{m_1}\] is the mass of one and \[{m_2}\] is the mass of the other, \[r\] is the distance between them.
hence, if we make \[r = \infty \], the force would be zero as would have
\[F = \dfrac{{G{m_1}{m_2}}}{{{\infty ^2}}} = 0\]
Hence, the correct answer is D.

Note: In actuality, the distance apart between two bodies cannot be infinity (as infinity is not a number). The concept of infinity in this case, means that the distance between the object are very far from each other relative to their own masses.