Question

Give the difference between gravitational constant (G) and acceleration due to gravity (g) with reference of their values

Answer 1

Hint: According to the concept of gravitational force and gravity, we can differentiate between the gravitational constant and acceleration due to gravity.

Formula Used: Formulas to consider:
${F_{grav}} \propto \dfrac{{{m_1} \times {m_2}}}{{{r^2}}}$ where m represents masses of different objects and r, the distance between them.
From newton’ second law of motion: force exerted is equal to the product of its mass and acceleration

Complete step by step answer:The concept of Gravitation was discovered by Newton.
Gravitation is a universal force existing between two bodies. It is directly proportional to the product of masses and inversely proportional to the square of distance between them.
Gravity is a strong gravitational force existing between the earth and any object.
Gravitational constant:
It is represented by G.
According to the definition gravitational force is represented as:
${F_{grav}} \propto \dfrac{{{m_1} \times {m_2}}}{{{r^2}}}$
Gravitational constant is used as the proportionality constant here to remove the sign of proportionality.
$
  {F_{grav}} = \dfrac{{G \times {m_1} \times {m_2}}}{{{r^2}}} \\
   \Rightarrow G = \dfrac{{{F_{grav}} \times {r^2}}}{{{m_1} \times {m_2}}} \\
 $
Using this formula we can define G and also find its dimensions.
If distance and the masses become 1, g will be equal to the gravitational force. So, it can be defined as:
Gravitational constant is equal to the gravitational force existing between two unit masses separated by a unit distance.
Its dimensions can be calculated as:
$
  G = \dfrac{{{F_{grav}} \times {r^2}}}{{{m_1} \times {m_2}}} \\
  G = \dfrac{{\left\{ {\left[ {ML{T^{ - 2}}} \right] \times {{\left[ L \right]}^2}} \right\}}}{{\left[ M \right] \times \left[ M \right]}} \\
  G = \left[ {{M^{ - 1}}{L^3}{T^{ - 2}}} \right] \\
 $
Its SI value is $6.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}$
Acceleration due to gravity:
It is represented by g.
According to Newton’s second law of motion force exerted on a body is given as:
F = ma where m is the mass and a is its acceleration.
But when this body is under the force of gravity (like in the case of its fall), the acceleration experienced is due to gravity, so the equation becomes:
F = mg where m is the mass of the body and g, acceleration due to gravity.
$ \Rightarrow g = \dfrac{F}{m}$
Using this formula we can define g and also find its dimensions.
If the mass of the body is 1 then g will be equal to the force exerted, so it can be defined as:
Acceleration due to gravity is equal to the force exerted per unit mass on the body falling under gravity.
Its dimensions can be calculated as:
$
  g = \dfrac{F}{m} \\
  g = \dfrac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ M \right]}} \\
  g = \left[ {L{T^{ - 2}}} \right] \\
 $
Its SI value is $9.8m/{s^2}$

Note: We use the term unit to represent the value 1.
We generally represent the dimensions in the square brackets. The main or basic dimensions are mass represented by M, length represented by L and time represented by T.
G is a universal constant and has a fixed value at all the positions but g can vary from one place to another.