Question

State the universal law of gravitation. Write the mathematical expression of this law.

Answer 1

Hint: The law of universal gravitation or the universal law of gravitation is related to the masses and the distance between any two bodies in the universe. It is directly proportional to the product of the masses between which it acts and the universal gravitational constant G.

Formula used:
$F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}$.

Complete step-by-step answer:
The universal law of gravitation states that any two objects with mass in the universe get attracted by a unique force that is directly proportional to the masses of the two objects. Additionally, it is inversely proportional to the square of the distance between the two objects it acts on as well.
Mathematically,
$F\alpha \dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}$
The proportionality can be removed from the formula by placing a proportionality constant named $G$, also called as universal gravitational constant. It is defined as the force between any two bodies which are separated by unit distance.
the final form of the formula turns into,
$F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}$
Where, $G$ is the proportionality constant or universal gravitational constant,
${{m}_{1}},{{m}_{2}}$ are the masses of the two objects, and
$r$ is the distance between the two objects.

Additional Information:
The universal law of gravitation is first stated by Isaac Newton in the year 1687. This law is similar to the coulomb’s law of electric charges. The only difference is we use coulomb constant in place of gravitational constant and product of two charges instead of product of two masses. The value of the universal gravitational constant is given by $G=6.674\times {{10}^{-11}}{{m}^{3}}k{{g}^{-1}}{{s}^{-2}}$.

Note: The universal law of gravitation is only applicable to objects with mass. If any object travels with a velocity near to light velocity, the law is not applicable. Also, this law is not applicable near places where light bends like black holes. Keep in mind that the law of gravitation is not applicable when one of the objects is too massive.