Question

How do you define gravitational constant? What are its values in C.G.S. and M.K.S. system? Why is it known as universal constant?

Answer 1

1.Newton's law of gravitation states that every particle of matter in the universe attracts every other particle with a force that varies directly as the product of the masses of two particles and inversely as the square of the distance between them.

2. Mathematically,

$$\begin{gathered} Gravitationalforce, \\ F\alpha M_1\times M_2 \\ Also,F\alpha \frac{1}{R^2} \\ where, \\ {M}_1\to Massof{1}^{st}body \\ {M}_2\to Massof{2}^{nd}body \\ R\to Dis\tan cebetweenboththebodies \\ Combiningboth,weget \\ F\alpha \frac{M_1\times M_2}{R^2} \\ or \\ F=G\times \frac{M_1\times M_2}{R^2} \\ where, \\ G\to Universalgravitationalcons\tan t \end{gathered}$$

3.We can say that G is the amount of gravitational force exerted when two masses of 1 kg each are kept at a distance of 1 m from each other.

$$\begin{gathered} If{M}_1=M_2=1kg \\ Also,R=1m \\ F=G\times \frac{1\times 1}{1^2} \\ =G \end{gathered}$$

4. In other words,

$$\begin{gathered} G=\frac{F\times r^2}{M_1\times M_2} \\ M.K.S.UnitofG=\frac{(UnitofF)\times {(Unitofr)}^2}{{(Unitofmass)}^2}=\frac{Newton\times metr{e}^2}{ki\log ra{m}^2} \\ =N{m}^{2}k{g}^{-2} \end{gathered}$$

5. Value of G

$G=6.6\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Converting in C.G.S. units

$$\begin{gathered} G=6.6\times {10}^{-11}\times ({10}^{5}dyne)\times {({10}^{2}cm)}^2\times {\left({10}^{3}g\right)}^{-2}=6.6\times {10}^{-11+5+4-6}dynec{m}^2{g}^{-2} \\ =6.6\times {10}^{-8}dynec{m}^2{g}^{-2} \end{gathered}$$

6. G is known as a universal constant as the value of G is independent of the mass, place, location, or any physical quantity.