Question

A string of cross section $2c{m}^2$ is doubled in length by the application of a longitudinal force $2\times {10}^5$ dynes. The young's modulus is

• A. ${10}^{7}dy/c{m}^2$
• B. ${10}^{5}dy/c{m}^2$
• C. ${10}^{4}dy/c{m}^2$
• D. $100dy/c{m}^2$

Answer 1

Answer: (B)

${10}^{5}dy/c{m}^2$

$\begin{array}{c}\text{Cross section Area}=2{cm}^2\\ =2\times {10}^{-4}{m}^2\\ \text{Length is doubled so elongation}\Delta l=2l-l=l\\ \text{Force}=2\times {10}^5\text{dyne.}\end{array}$

$\begin{array}{c}y=\frac{2\times {10}^5\mathrm{dyne}}{2{cm}^2}\left(\frac{l}{\delta l}\right)(\because y=\frac{Fl}{A\Delta l})\\ y={10}^{5}dyne/{cm}^2\end{array}$