Gravitational potential at any point is defined as to carry a unit mass from infinity to that point

Gravitational Potential:
Gravitational potential is a concept used in physics to describe the potential energy of an object due to its position in a gravitational field. It is defined as the amount of work done in bringing a unit mass from infinity to a specific point in the field.

Understanding the Options:
In the given question, we are asked to determine which option correctly defines the gravitational potential due to the gravitational force on the Earth. Let's analyze each option to understand their meanings:

a) Potential energy multiplied by the mass of the object: This option suggests that the gravitational potential is equal to the potential energy multiplied by the mass of the object. However, this is not the correct definition of gravitational potential.

b) Potential energy of the mass placed at that point: This option suggests that the gravitational potential is equal to the potential energy of the mass placed at that point. While potential energy is related to gravitational potential, this option does not specifically define the gravitational potential.

c) Numerically equal to the potential energy: This option suggests that the gravitational potential is numerically equal to the potential energy. However, this is not the correct definition of gravitational potential.

d) Potential energy of a unit mass at that point: This option suggests that the gravitational potential is equal to the potential energy of a unit mass at that point. This is the correct definition of gravitational potential.

Explanation:
Gravitational potential is defined as the potential energy per unit mass at a specific point in a gravitational field. It represents the amount of potential energy possessed by a unit mass at that point. The gravitational potential due to the gravitational force on the Earth is the potential energy of a unit mass placed at a specific point on or near the Earth's surface.

By using the definition of gravitational potential, we can calculate the gravitational potential energy for an object of mass 'm' at a certain point by multiplying the gravitational potential by the mass of the object. Therefore, option 'D' is the correct answer as it accurately defines the gravitational potential due to the gravitational force on the Earth.