Question

Young's modulus of steel is $2.0\times {10}^{11}N/m^2.$ Express it in $dyne/c{m}^2.$

• A. $2.0\times {10}^{12}dyne/c{m}^2$
• B. $2.0\times {10}^{11}dyne/c{m}^2$
• C. $4.0\times {10}^{12}dyne/c{m}^2$
• D. $4.0\times {10}^{11}dyne/c{m}^2$

Answer 1

The correct option is A $2.0\times {10}^{12}dyne/c{m}^2$

Dyne is the CGS unit of Force.
Dimension of force is $\left[ML{T}^{-2}\right]$.
Thus, dimension of Young's modulus is $|F/A|=$$M{L}^{-1}{T}^{-2}$
$1kg=1000g,1m=100cm$
Thus, $2\times {10}^{11}N/m^2=2\times {10}^{11}\times \left(1000g\right)\times (100cm{)}^{-1}\times 1s^{-2}$
$=2\times {10}^{11}\times 10=2\times {10}^{12}dyne/c{m}^2$