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

The unit of Young's modulus is N/m². This suggests that it has dimensions of $\frac{\text{ Force }}{(\text{ distance }{)}^2}$

$\begin{array}{l}\text{ Thus, }\left[Y\right]=\frac{\left[F\right]}{L^2}=\frac{ML{T}^{-2}}{L^2}=M{L}^{-1}{T}^{-2}\cdot \mathrm{N}/{\mathrm{m}}^2\text{ is in SI units. }\\ \begin{array}{rl} & \text{ So, }1\mathrm{N}/{\mathrm{m}}^2=\left(1\mathrm{kg}\right)\left(1\mathrm{m}{)}^{-1}\right(1\mathrm{s}{)}^{-2}\\ & \text{ and }1\mathrm{dyne}/{\mathrm{cm}}^2=\left(1\mathrm{g}\right)\left(1\mathrm{cm}{)}^{-1}\right(1\mathrm{s}{)}^{-2}\\ & \text{ so, }\begin{array}{rl} & \frac{1\mathrm{N}/{\mathrm{m}}^2}{1\mathrm{dyne}/{\mathrm{cm}}^2}=\left(\frac{1\mathrm{kg}}{1\mathrm{g}}\right){\left(\frac{1\mathrm{m}}{1\mathrm{cm}}\right)}^{-1}{\left(\frac{1\mathrm{s}}{1\mathrm{s}}\right)}^{-2}\\ =& 1000\times \frac{1}{100}\times 1=10\\ \text{ or }& 1\mathrm{N}/{\mathrm{m}}^2=10\mathrm{dyne}/{\mathrm{cm}}^2\\ \text{ or }& 19\times {10}^{10}\mathrm{N}/{\mathrm{m}}^2=19\times {10}^{11}\text{ dyne }/{\mathrm{cm}}^2\end{array}\end{array}\end{array}$