Question

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\, mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)

• A. $2.77 \times 10^{-2} mm$
• B. $6.9 \times 10^{-2} mm$
• C. $6.06 \times 10^{-2} mm$
• D. $3.0 \times 10^{-2} mm$

Answer 1

Answer: (B)

$ Y =\frac{ F / A }{\frac{\Delta \ell}{\ell}} $
$ \Rightarrow F =\frac{ YA }{\ell} \Delta \ell $
$ \left(\frac{ A \Delta \ell}{\ell}\right)_1=\left(\frac{ A \Delta \ell}{\ell}\right)_2 $
$ \Rightarrow \frac{\Delta \ell_2}{\Delta \ell_1}=\frac{ A _1}{ A _2} \times \frac{\ell_2}{\ell_1} $
$ \Rightarrow \frac{\Delta \ell_2}{0.2}=\frac{1}{2.4 \times 2.4} \times \frac{2}{1} $
$\Rightarrow \Delta \ell_2=6.9 \times 10^{-2} mm$