Dyne and Newton both the words are well known to us. We all study about that in class 9. But If we have remembered that there would be a relation exist between Dyne and Newton. So before we start discussing about relation. we should have recall both the terms Dyne and Newton in detail. After that we not only established the relation between Newton and Dyne but also derive the relation.
What is Newton?
Newton is the S.I unit of force. Which is denoted by N. Apart from this concept. Newton was a scientist. He discovered gravitation, and also very famous three laws of motion. He also write some novel on optics, calculus etc.
One Newton is defined as: A body of mass 1 kg travelling with the acceleration of 1m/s2. means 1 N = 1kg ✖ 1m/s2.
F = ma
Newton = kg . m/s2.
What is Dyne?
It is the C.G.S unit of force. It is denoted by ”Dyne”. If we define one dyne then it is a body of one gram of mass travelling with the acceleration of one centimeter per second square. i.e, 1 Dyne = 1g ✖ 1cm/s2.
F = ma
Dyne = 1g . cm/s2
Relation between Dyne and Newton
The mathematical relation between Newton and Dyne is, one newton is equal to the ten to the power five dyne. i.e,
1 Newton = 10^5 Dyne
In other words, the main relation between newton and dyne is both the term has same property. Means both have a unit of Force. But the difference is one have S.I unit and other is C.G.S unit.
- S.I unit of force is Newton
- C.G.S unit of force is Dyne.
Derivation of relation between Newton and Dyne
Here below are the derivation of relation between Dyne and Newton.
As we know that Force is the product of mass and acceleration. That means in mathematical terms F = ma. we also studied that force is the cross product of mass and acceleration.
F = ma
Force = mass x acceleration
Force = kg x m/s2 ————— (1)
Now, change it in C.G.S unit. then,
Force = 1000 gram x 100 cm/s2 ———— (2)
From equ. 1 and 2 we get,
1 kg x 1 m/s2 = 1000 gram x 100 cm/s2
1 Newton (from the definition of one newton) = 1000 x 100 x 1 gram . 1cm/s2
1 Newton = 10^5 x 1 gram . 1 cm/s2
1 Newton = 10^5 x 1 Dyne (from the definition of 1 Dyne)
1 Newton = 10^5 Dyne
Hence, the relation between Dyne and Newton is 1 Newton = 10^5 Dyne.