Question

To determine the Youngs modulus of a wire,the formula is $Y=\frac{F}{A}\times \frac{\Delta L}{L}$; 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 :

• A. 1
• B. 10
• C. 0.1
• D. 0.01

Answer 1

Answer: (C)

0.1

Young's modulus, $Y=\frac{F}{A}\times \frac{\Delta L}{L}$

As the both $\Delta L$ and $L$ have same unit i.e. unit of length, so the term $\frac{\Delta L}{L}$ will be unit-less.

Thus, unit of Young's modulus becomes unit of force divided by unit of area.

Therefore, CGS unit of Y is $dyne/c{m}^2$ and MKS unit of it is $N/m^2$.

Thus, $1dyne/c{m}^2=\frac{{10}^{-5}N}{({10}^{-2}{)}^2{m}^2}=0.1N$

(note : $1N={10}^{5}dyne$)