Question

The extension of wire by application of load is $0.3cm$ The extension in a w wire of same material but of double the length and half the radius of cross section by the same load will be in (cm)

• A. $0.3$
• B. $0.6$
• C. $0.2$
• D. $2.4$

Answer 1

The correct option is D $2.4$

given, extension of wire by application of a load is $0.3cm$

Now, on doutling length and making the radics half of its origenal, we get

$\begin{array}{cc}{A}_f& =\frac{A_i}{4}{L}_f=2L\\ F& =Y{A}_i\left(\frac{0\cdot 3}{L}\right)\\ F& =Y\frac{A_i}{4}\left(\frac{\Delta L}{2L}\right)\Rightarrow \frac{F}{0.3}\times \frac{\Delta L}{8}\\ & \therefore \Delta L=2\cdot 4cm\end{array}$