Question

Young's modulus of steel is $19\times 10^{10}N/m^2$. Express it as $x\times 10^{11}\text{dyne}/c{m}^2$. Here dyne is the CGS unit of force. The value of $x$ is____.

Answer 1

Answer: 19

The unit of Young's modulus is $N/m^2$.
This suggests that it has dimensions of $\frac{\text{ Force }}{(\text{ distance }{)}^2}$.
Thus, $[Y]=\frac{[F]}{L^2}=\frac{ML{T}^{-2}}{L^2}=M{L}^{-1}{T}^{-2}\cdot N/m^2$ is in SI units.
So, $1N/m^2=(1kg)(1m{)}^{-1}(1s{)}^{-2}$
and 1 dyne $/c{m}^2=(1g)(1cm{)}^{-1}(1s{)}^{-2}$
so, $\frac{1N/m^2}{1\text{ dyne }/c{m}^2}=\left(\frac{1kg}{1g}\right){\left(\frac{1m}{1cm}\right)}^{-1}{\left(\frac{1s}{1s}\right)}^{-2}$
$=1000\times \frac{1}{100}\times 1=10$
or $1N/m^2=10$ dyne $/c{m}^2$
or $19\times 10^{10}N/m^2=19\times 10^{11}$ dyne $/c{m}^2$.