Question

(a) State the universal law of gravitation. Name the scientist who gave this law.
(b) Define gravitational constant. What are the units of gravitational constant.

Answer 1

Hint: From the concept of law of gravitation, we know that two bodies present in this universe attract them with a force of attraction. We will write the expression for the gravitational constant to define it and to find out its unit.

Complete step by step answer:
(a) Using the concept of gravitational force, we can write:
\[F \propto \dfrac{{{m_1}{m_2}}}{{{r^2}}}\]
Here \[{m_1}\] is the mass of the first body, \[{m_2}\] is the mass of the second body and r is the distance between the centres of these two masses.
This law is given by Isaac Newton and also known as Newton gravitational law.
(b) We can remove the sign of proportionality by introducing a constant.
\[F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}}\]
Here G is introduced due to proportionality sign and called a gravitational constant.
We can rewrite the above equation in such a way that the value of gravitational constant G can be evaluated.
\[G = \dfrac{{F{r^2}}}{{{m_1}{m_2}}}\]
The gravitational constant is equal to the value of force present between two particles having a unit value of mass and unit distance by which they are kept apart.
We know that the unit of force, mass and radius is Newton, kilogram and metre. Therefore, we can write the unit of gravitational constant G as below:
Unit of \[
G = \dfrac{{{\rm{N}} \cdot {{\rm{m}}^2}}}{{{\rm{kg}} \cdot {\rm{kg}}}}\\
\therefore G = {\rm{N}}{{\rm{m}}^2}{\rm{k}}{{\rm{g}}^2}
\]
Note: We can further resolve the unit Newton into its base units (kg, m, s) which is equal to kilogram-metre per second square \[\left( {{\rm{kg}}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {{{\rm{s}}^2}}}} \right.
 } {{{\rm{s}}^2}}}} \right)\]. The magnitude of the force between a pair of an object is dependent on the distance by which they are kept apart; that is if the distance is more than the magnitude of force will be less and vice-versa.