Question

When load is applied to a wire, the extension is $3mm.$ The extension in the wire of same material and length but half the radius extended by the same load is :

• A. $0.75mm$
• B. $6mm$
• C. $1.5mm$
• D. $12.0mm$

Answer 1

The correct option is D $12.0mm$

$Y=\frac{Fl}{A\left(△l\right)}$

$△l=\frac{Fl}{Y\pi R^2}$

$So,△l\alpha \frac{1}{R^2}$

$\frac{△l_1}{△l_2}=\frac{r_2^2}{r_1^2}=(\frac{1}{2}{)}^2=\frac{1}{4}(\because \frac{r_1}{r_2}=2)$

$4△l_1=△l_2$

$So,△l_2=4\left(3\right)$

$=12mm$