Question

Two wires of the same material have diameter in the ratio 2:1 and length in the ratio 1:2. If they are stretched by the same force, their elongation will be in the ratio

• A. 8:1
• B. 1:8
• C. 2:1
• D. 1:4

Answer 1

The correct option is B

1:8

$\frac{r_1}{r_2}=\frac{2}{1};\frac{I_1}{I_2}=\frac{1}{2}Y=\frac{FI}{\pi r^2.y}\Delta I=\frac{FI}{\pi r^2.y}\Delta I\propto \frac{1}{r^2}{\left(\Delta I\right)}_1:(\Delta I{)}_2=\frac{I_1}{r_1^2}:\frac{I_1}{r_2^2}=\frac{1}{4}:\frac{2}{1}=1:8$