Question

Two wires of the same material have masses in the ratio 3:4. The ratio of their extensions under the same load if their lengths are in the ratio 9:10 is

• A. 5 : 3
• B. 27 : 40
• C. 6 : 5
• D. 27 : 25

Answer 1

The correct option is B 27 : 40

$Y=\frac{FL}{\left(Ae\right)}$

For same material $Y$ is constant and $A$ is constant for two similar wires.

$\frac{FL}{e}=$ constant

here, $F=mg$

$\frac{e_1}{e_2}=\frac{m_1}{m_2}\times \frac{L_1}{L_2}$

$=\frac{3}{4}\times \frac{9}{10}$

$=\frac{27}{40}$