Question

Derive the relation between C.G.S and S.I unit of force.

Answer 1

Hint: In this question, we use the dimension of force. Using these dimensions and the units, we will get the required result. Further, we will also discuss the basic concept of force and the different laws of motion, for our better understanding.
Formula used:
$\left[ {{L^1}{M^1}{T^{ - 2}}} \right]$

Complete answer:
As we know that the S.I unit of force is Newton, represented by N.
Let one Newton (S.I) be equal to x dyne (C.G.S)
As we know that the dimension of force is given as:
$\left[ {{L^1}{M^1}{T^{ - 2}}} \right]$
Using the relation between the Newton and dyne we have:
$\left[ {L_1^1M_1^1T_1^{ - 2}} \right] = x\left[ {L_2^1M_2^1T_2^{ - 2}} \right]$
$x = {\left( {\dfrac{{{L_1}}}{{{L_2}}}} \right)^1}{\left( {\dfrac{{{M_1}}}{{{M_2}}}} \right)^1}{\left( {\dfrac{{{T_1}}}{{{T_2}}}} \right)^{ - 2}}$
Now, putting the values of S.I units and C.G.S unit in the above equation, we get:
$\eqalign{& x = {\left( {\dfrac{m}{{cm}}} \right)^1}{\left( {\dfrac{{kg}}{g}} \right)^1}{\left( {\dfrac{s}{s}} \right)^{ - 2}} \cr
  & \Rightarrow x = {10^2} \times {10^3} \cr
  & \Rightarrow x = {10^5} \cr
  & \therefore 1N = {10^5}dyne \cr} $
Therefore, we get the relation between the S.I unit and C.G.S unit of force in the above result.

Additional information:
Force is simply any push or pull. The S.I unit of force is Newton represented by N.The acceleration is defined as the increase in the velocity of an object. The acceleration is measured in meters per Second Square.
There are three laws of motions given by Newton. These laws of motion relate an object's motion to the forces acting on it.
First law of motion states that an object continues to be in rest or in motion in a particular direction until and unless any external force is applied on it.
 In the second law of motion, the force on an object is equal to its mass times its acceleration. This law also gives the relation of momentum and force.
In the third law of motion, every action has an equal and opposite reaction.

Note:
Force applied on an object changes its motion, speed, direction and also its shape. There is a very small difference between the force applied and the pressure applied on an object. Pressure is always given as the force per unit area.