Question

How to prove $1\,gf = 980\,dyne$ ?

Answer 1

Hint: Let us first understand about the units of measurement i.e. dyne and 1gf (one gram force). We can further continue to know about what force is and how SI unit of energy is defined using this. So basically force (F) can be described as a push or pull on an object. A force can cause an object with mass to change its velocity. It has both magnitude and direction, making it a vector quantity. SI unit of force is newton (N).

Complete step by step answer:
The dyne is defined as "the force required to accelerate a mass of one gram at a rate of one centimetre per second squared".
\[1\,dyne = 1\,g.cm.{s^{ - 2}} \\
\Rightarrow 1\,dyne = {10^{ - 5}}\,kg.m.{s^{ - 2}} \\
\Rightarrow 1\,dyne = {10^{ - 5}}\,N\]

The gram-force is a metric unit of force (gf). The gram-force is equal to a mass of one gram multiplied by acceleration due to gravity on Earth i.e. 9.8 meter per second².
\[1\,gf = 1g \times 9.8\,m{s^{ - 2}} \\
\Rightarrow 1\,gf = 1g \times 980\,cm.{s^{ - 2}} \\
\Rightarrow 1\,gf = 980\,g.cm.{s^{ - 2}} \\
\therefore 1\,gf = 980\,dyne \\ \]
Hence Proved.So we can conclude $1\,gf = 980\,dyne$.

Note:The dyne per centimetre is generally used to measure surface tension. The gravity of Earth (g) is the net acceleration on objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity. In air or water, apparent strength of gravity is less (as measured by an object's weight). The value of g is not the same everywhere, it varies on the basis of altitude. The value of g is more at the poles and less at the equator.