Question

A wire extends by 1 mm when a force is applied. What will be the elongation(in mm) in wire of same material if the force is doubled on the wire of same length and half the radius?

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

The correct option is A 8

a) say l= elongation; L= original length; Y= modulus of elasticity. Then from Hooke's law
$l=\frac{FL}{\pi r^{2}Y}=l\propto \frac{F}{r^2}$ (Y and L are constant)
$\frac{l_2}{l_1}=\frac{F_2}{F_1}\times (\frac{r_1}{r_2}{)}^2=2\times (2{)}^2=8\Rightarrow l_2=8l_1=8\times$1=8mm