Question

How to prove $1gf=980dyne$?

Answer 1

Step1: gf and dyne

1. One gram-force (gf) is equal to a mass of one gram multiplied by the standard acceleration due to gravity on Earth's surface.
2. Dyne is the CGS unit of force. One dyne equal to the force that would give a free mass of one gram an acceleration of one centimeter per second square.
3. $1dyne=0.00001newton$

Step2: Formula Used

1. $1dyne$ is the force that would give a free mass of $1g$ an acceleration of $1cm/s^2$. Mathematically, it is expressed as $1dyne=1g\times 1cm/s^2$
2. gram-force (gf) is equal to a mass of one gram multiplied by the standard acceleration due to gravity on Earth's surface $1gf=1g\times 9.8m/s{}^2$

Step3: Solution

Calculate the relation using the above formulas.

$\begin{array}{rcl}1gf& =& 1g\times 9.8m/s^2\\ & =& 1g\times 980cm/s^2\left[\because 1m=100cm\right]\\ & =& 980dyne\left[\because gm/s{}^2=dyne\right]\end{array}$

Thus, $\mathbf{1}\mathbf{}\mathit{g}\mathit{f}\mathbf{=}\mathbf{980}\mathbf{}\mathit{d}\mathit{y}\mathit{n}\mathit{e}$