Question

to determine the youngs modulus of a wire, the formula is y = \\(\frac{f}{a}\times\frac{l}{\delta l}\\); where l = length, a = area of cross - section of the wire, \\(\delta l\\) = change in length of the wire when stretched with a force f. the conversion factor to change it from cgs to mks system is (1) 1 (2) 10 (3) 0.1 (4) 0.01

Explanation:

Step1: Recall CGS and MKS units

In CGS, force is dyne, length is cm and area is $cm^{2}$. In MKS, force is Newton, length is m and area is $m^{2}$.
1 dyne = $10^{- 5}$ N, 1 cm = $10^{-2}$ m.

Step2: Analyze the formula for Young's modulus $Y=\frac{F}{A}\times\frac{L}{\Delta L}$

The conversion of force from dyne to Newton: If $F$ is in dyne, to convert it to Newton, we multiply by $10^{-5}$.
The conversion of area from $cm^{2}$ to $m^{2}$: Since $1\ cm = 10^{-2}\ m$, then $1\ cm^{2}=(10^{-2})^{2}m^{2}=10^{- 4}m^{2}$.
The conversion of length and change - in - length from cm to m: multiply by $10^{-2}$.
When we convert the formula from CGS to MKS for Young's modulus, the conversion factor for $\frac{F}{A}$ is $\frac{10^{-5}}{10^{-4}} = 10^{-1}$.

Answer:

0.1