Question

If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be :

• A. $\frac{b^2}{2c}$
• B. $\frac{bc}{{2a}^2}$
• C. $\frac{{ba}^2}{2c}$
• D. $\frac{{2b}^{2}c}{a}$

Answer 1

The correct option is D $\frac{{2b}^{2}c}{a}$

$\Delta L=\frac{FL}{AY}$

Force on the Steel wire $=20N$

Elongation in the steel wire $=\frac{20\times l_s}{A_s{Y}_s}$

Force on the brass wire $=20N+20N=40N$

Elongation in the brass wire $=\frac{40\times l_b}{A_b{Y}_b}$

$\Rightarrow \frac{\Delta L_b}{\Delta L_s}=\frac{40}{20}\frac{L_b}{L_s}\frac{r_s^2}{r_b^2}\frac{Y_s}{Y_b}=\frac{2b^{2}c}{a}$