Question

A wire of length 2 mis made from $10c{m}^3$ of copper. A force Fis applied so that its length increases by 2 mm.Another wire of length 8 m is made from the same volume of copper. If the force is applied to it, its length will increase by

• A. 0.8 cm
• B. 1.6 cm
• C. 2.4 cm
• D. 3.2 cm

Answer 1

The correct option is D

3.2 cm

$l=\frac{FL}{AY}=\frac{F{L}^2}{\left(AL\right)Y}=\frac{F{L}^2}{VY};\therefore l\infty L^2\text{If volume of the wire remains constant}\to \frac{l_2}{l_1}={\left(\frac{L_2}{L_1}\right)}^2={\left(\frac{8}{2}\right)}^2=16$