A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{~mm}$. If same force is applied to another steel wire ' $\mathrm{B}$ ' of double the length and a diameter $2.4$ times that of the wire ' $\mathrm{A}$ ', the elongation in the wire ' $\mathrm{B}$ ' will be (wires having uniform circular cross sections)
Solution
<p>$\because$ $\Delta l = {{Fl(4)} \over {Y\pi {d^2}}}$</p>
<p>$${{\Delta {l_1}} \over {\Delta {l_2}}} = {{\Delta {l_1}} \over {d_1^2}} \times {{d_2^2} \over {{l_2}}}$$</p>
<p>${{0.2} \over {\Delta {l_2}}} = {1 \over 2} \times {(2.4)^2}$</p>
<p>$\Delta {l_2} = {{2 \times 0.2} \over {{{(2.4)}^2}}}$</p>
<p>$= 6.9 \times {10^{ - 2}}$ mm</p>
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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