Question

Convert Newton into dyne.

Answer 1

Hint: Newton is the unit of force in the MKS (or SI) system and dyne is the unit of force in the CGS system.

Complete step by step solution:
Newton is the unit of force in the MKS (or SI) system. Since force has the dimensions of $MLT^{-2}$, the unit Newton can also be written as $kgms^{-2}$.
Therefore, writing in the MKS system,
$1Newton=1kg.m.{{s}^{-2}}$
Now converting into the CGS system with the help of the known facts that
$1kg=1000gm$
$1m=100cm$
We get,
$1Newton=1kg.m.{{s}^{-2}}=1000gm.100cm.{{s}^{-2}}$
$\therefore 1Newton=100000gm.cm.{{s}^{-2}}={{10}^{5}}gm.cm.{{s}^{-2}}$ ---(1)
Now, we know that dyne is the unit of force in the CGS system,
$\therefore 1dyne=1gm.cm.{{s}^{-2}}$ --(2)
Now, using (1) and (2),
$1Newton={{10}^{5}}dyne$

Additional information:
The CGS system is not very widely used; however in Europe it is quite popular. It stands for centimetre-gram-second. In this system the unit dyne is quite popular in the measurement of force in many countries and especially in the measurement of pressure using the concept that pressure is force per unit area. In this system the unit of pressure then becomes dynes-$cm^{-2}$.
There is also another system of units known as the FPS system of units. It is used predominantly in the United States of America. It stands for Foot-Pound-Second. In this system, length is measured in feet, mass in pounds (lb) and time in seconds (s).
However, the most widely used and internationally accepted system of units is the SI system or MKS system of units.

Note: Students should keep the relation between Newton and dyne in mind since many questions can implement the usage of dyne just to confuse students. However, it is not mandatory to memorize the relation.
The student must practice converting between the systems of units efficiently using the simple method shown above. This is a much better way of learning and conversions can be made in less than half a minute in this way. This is actually the correct way of proceeding and not rote memorizing.