Question

What is the value of the universal gas constant? Write also its S.I. unit.

Answer 1

Hint: The universal gravitational constant is a constant of proportionality that remains the same throughout the whole universe. The universal gravitational constant acts as a proportionality factor to equate the gravitational force exerted by an object on another object with the product of their masses and the square of the distance between them.

Complete answer:
When Newton introduced his laws of motion in the Principia mathematical he also added a fourth law which governed the motion of astronomical objects through space. We call this fourth law the universal law of gravitational attraction. According to the law of gravitation, each mass in the universe exerts a net attractive force on every other mass in the direction of its own center of mass. Newton proposed that this force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the two. In mathematical terms these two statements could be represented as;
Proportionality of mass;
$ \Rightarrow {F_G} \propto M \times m$
And the inverse proportionality of the square of the distance between them;
\[ \Rightarrow {F_G} \propto \dfrac{1}{{{r^2}}}\]
Combining the two statements would require us to introduce a proportionality constant, converting the equation to;
$ \Rightarrow {F_G} = \dfrac{{GMm}}{{{r^2}}}$
Here $G$ is what we call the universal gravitational constant. Newton calculated the value of the universal gravitational constant to be equal to about;
$ \Rightarrow G = 6.67408 \times {10^{ - 11}}{m^3}K{g^{ - 1}}{s^{ - 2}}$
 It is partly because $G$ is such a small number that our normal day to day objects do not seem to exert any force on each other.
There is no such single unit issued for the universal gravitational constant as of yet. Hence, the S.I. unit of $G$ is a compound unit comprising multiple units. As shown above the S.I. a unit of the gravitational constant is a compound unit of mass length and time raised to different indices. Each of these individual units are either defined as the ratios of fundamental constants or are represented by heavily preserved and secured objects as a standard of reference. Thus, the universal gravitational constant has the S.I unit value of ${m^3}K{g^{ - 1}}{s^{ - 2}}$ .

Note:
Henry Cavendish in his famous two balls and a weighing scale was able to accurately measure the mass of the earth using Newton’s laws in a shed in his backyard. He calculated the mass of the earth to be approximately $5.972 \times {10^{24}}Kg$.