Question

A wire of length 1 m and radius 1 mm is subjected to a load. The extension is 'x'. The wire is melted and then drawn into a wire of square cross-section of side 1 rnm. What is its extension under the same load ?

• A. ${\pi }^{2}x$
• B. $\pi x^2$
• C. $\pi x$
• D. $\pi /x$

Answer 1

The correct option is A ${\pi }^{2}x$

Solution

we know,

r(Young Modules) = $\frac{stress}{strain}$

$\to r=\frac{\left[\frac{L}{\pi (1{)}^2}\right]}{\left(\frac{X}{1}\right)}$ [L is the load]

$\Rightarrow r=\frac{L}{\pi X}$

As r is the properly of wire, if will remain

same even after meeting So,

$r=\frac{\frac{L}{(1{)}^2}}{\frac{X^{\prime }}{l^{\prime }}}$

As volume will remain same, $\left(1\right)\left[\pi \right(1{)}^2]=l^{\prime }(1{)}^2$

So, $\Rightarrow \frac{L}{\pi X}=\frac{\frac{L}{X^{\prime }}}{\pi }\Rightarrow X^{\prime }={\pi }^{2}X$

Option - A is correct.