Question

State universal law of gravitation and derive the expression for force between two objects of mass $$m_1$$ and $$m_2$$ separated by distance ‘$$d$$’.

Answer 1

Hint: Universal law of gravitation was proposed by newton.
It gives the gravitational force between two point masses.

Complete step by step answer:
According to Newton’s Universal law of gravitation:
Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of masses of particles and inversely proportional to the square of the distance between them.

If $$m_1$$and $$m_2$$are two point masses separated by a distance $$d$$, the gravitational force of attraction $$F$$ is given by :
$$\begin{gathered} F\propto m_1{m}_2 \\ F\propto {\displaystyle \frac{1}{d^2}} \end{gathered}$$
Combining the above two equations we get :
$$\begin{gathered} F\propto {\displaystyle \frac{m_1{m}_2}{d^2}} \\ F=G{\displaystyle \frac{m_1{m}_2}{d^2}} \end{gathered}$$
Where $G$ is called Universal Gravitational Constant. The value of $G$ is :
$$G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$$

Additional Information:
Properties of Gravitational Force
1. It is always attractive, the weakest force in nature and is of conservative type.
2. It is a central force. (Central force is a position dependent force and it acts along the line joining the two bodies.)
3. It doesn’t depend on the medium between the two bodies.
4. The gravitational attractive force between two bodies doesn’t depend on the presence of other third bodies.
5. It obeys the principle of superposition i.e., the law of vector addition.

Note:
Newton’s law of Gravitation is applied on the point masses but it can also be applied for the bodies of any shape provided the separation between the bodies is greater than the size of the bodies.