Question

Write relation between g and G.

Answer 1

Hint: G is the force between two bodies of unit mass separated by distance r. G is known as a universal gravitational constant. g is the acceleration produced in a body falling under the action of gravitational pull of the earth. Here g is called acceleration due to gravity. Equation for g is $F=mg$ and Equation for G is $F=G\dfrac{{{m}_{1}}m}{{{r}^{2}}}$.

Complete step by step answer:
The gravitational force between two masses m1 and m2 is proportional to the product of mass and is inversely proportional to square of the distance (r) apart,
$\begin{aligned} & F\propto \dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}} \\\ & F=G\dfrac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}} \\\ \end{aligned}$
Gravity – the force of attraction exerted by the earth on other objects is called gravity. The direction of force F is towards the center of the earth which is called the vertically downward direction force. This force is also called gravitational force and given as -
$F=mg$
Let m be the mass of an object and m1 be the mass of earth. And r is the radius of the earth.
$\begin{aligned} & F=G\dfrac{{{m}_{1}}m}{{{r}^{2}}} \\\ & mg=G\dfrac{{{m}_{1}}m}{{{r}^{2}}} \\\ & g=G\dfrac{{{m}_{1}}}{{{r}^{2}}} \\\ \end{aligned}$
The term $G\dfrac{{{m}_{1}}}{{{r}^{2}}}$is called acceleration due to gravity and is denoted by the letter g.
Hence relation between g and G is $g=G\dfrac{{{m}_{1}}}{{{r}^{2}}}$

Note: Students should remember that g is much different from G.
The value of g is $g=9.8m/{{s}^{2}}$ or for simplicity we use$g=10m/{{s}^{2}}$.
And the value of G is so small and becomes appreciable only if two bodies have large masses. And approximately equal to $6.674\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}$