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 $F=G{\displaystyle \frac{m_{1}m}{r^2}}$.

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,
$\begin{array}{rl}& F\propto {\displaystyle \frac{m_1{m}_2}{r^2}}\\ & F=G{\displaystyle \frac{m_1{m}_2}{r^2}}\end{array}$
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.
$\begin{array}{rl}& F=G{\displaystyle \frac{m_{1}m}{r^2}}\\ & mg=G{\displaystyle \frac{m_{1}m}{r^2}}\\ & g=G{\displaystyle \frac{m_1}{r^2}}\end{array}$
The term $G{\displaystyle \frac{m_1}{r^2}}$is called acceleration due to gravity and is denoted by the letter g.
Hence relation between g and G is $g=G{\displaystyle \frac{m_1}{r^2}}$

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 $6.674\times {10}^{-11}N{m}^2/k{g}^2$