Question

In an experiment, bras and steel wires of length lm each with areas of cross section $1m{m}^2$ are used. the wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of $0.2mm$ is :
(Given, the Young's Modulus for steel and brass are respectively, $120\times {10}^{9}N/m^2$ and $60\times {10}^{9}N/m^2$)

• A. $0.2\times {10}^{6}N/m^2$
• B. $4.0\times {10}^{6}N/m^2$
• C. $1.8\times {10}^{6}N/m^2$
• D. $1.2\times {10}^{6}N/m^2$

Answer 1

Answer: (B)

$4.0\times {10}^{6}N/m^2$

$k_1=\frac{y_1{A}_1}{{\ell }_1}=\frac{120\times {10}^9\times A}{1}$
$k_2=\frac{y_2{A}_2}{{\ell }_2}=\frac{60\times {10}^9\times A}{1}$
$k_{eq}=\frac{k_1{k}_2}{k_1\times k_2}=\frac{120\times 60}{180}\times {10}^9\times A$
$k_{eq}=40\times {10}^9\times A$
$F=k_{eq}\left(x\right)$
$F=(40\times {10}^9)A.(0.2\times {10}^{-3})$
$\frac{F}{A}=8\times {10}^{6}N/m^2$
No option is matching.Hence question must be bonus.