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One end of a steel wire is fixed to the ceiling of a moving elevator. A load of 20 kg hangs from the other end. If the elevator is moving up with an acceleration 1 m/s2 and Area of cross- section of wire is 2 cm2 then find the longitudnal strain in the wire.[Take g=10 ms−2,Y=2×1011 Nm−2 ] |
Answer» <p>One end of a steel wire is fixed to the ceiling of a moving elevator. A load of <span class="mjx-chtml" id="MathJax-Element-1-Frame"><span class="mjx-math" id="MJXc-Node-126627"><span class="mjx-mrow" id="MJXc-Node-126628"><span class="mjx-mn" id="MJXc-Node-126629"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">20</span></span><span class="mjx-mtext" id="MJXc-Node-126630"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-mtext" id="MJXc-Node-126631"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">kg</span></span></span></span></span> hangs from the other end. If the elevator is moving up with an acceleration <span class="mjx-chtml" id="MathJax-Element-2-Frame"><span class="mjx-math" id="MJXc-Node-126632"><span class="mjx-mrow" id="MJXc-Node-126633"><span class="mjx-mn" id="MJXc-Node-126634"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mtext" id="MJXc-Node-126635"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-msubsup" id="MJXc-Node-126636"><span class="mjx-base"><span class="mjx-mtext" id="MJXc-Node-126637"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">m/s</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.71em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-126638" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span> and Area of cross- section of wire is <span class="mjx-chtml" id="MathJax-Element-3-Frame"><span class="mjx-math" id="MJXc-Node-126639"><span class="mjx-mrow" id="MJXc-Node-126640"><span class="mjx-mn" id="MJXc-Node-126641"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mtext" id="MJXc-Node-126642"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-msubsup" id="MJXc-Node-126643"><span class="mjx-base"><span class="mjx-mtext" id="MJXc-Node-126644"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">cm</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-126645" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span> then find the longitudnal strain in the wire.<br><br>[Take <span class="mjx-chtml" id="MathJax-Element-4-Frame"><span class="mjx-math" id="MJXc-Node-126646"><span class="mjx-mrow" id="MJXc-Node-126647"><span class="mjx-mi" id="MJXc-Node-126648"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.003em;">g</span></span><span class="mjx-mo MJXc-space3" id="MJXc-Node-126649"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3" id="MJXc-Node-126650"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span><span class="mjx-mtext" id="MJXc-Node-126651"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-msubsup" id="MJXc-Node-126652"><span class="mjx-base"><span class="mjx-mtext" id="MJXc-Node-126653"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">ms</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" id="MJXc-Node-126654" style=""><span class="mjx-mrow" id="MJXc-Node-126655"><span class="mjx-mo" id="MJXc-Node-126656"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn" id="MJXc-Node-126657"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-mo" id="MJXc-Node-126658"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1" id="MJXc-Node-126659"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.182em;">Y</span></span><span class="mjx-mo MJXc-space3" id="MJXc-Node-126660"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3" id="MJXc-Node-126661"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2" id="MJXc-Node-126662"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">×</span></span><span class="mjx-msubsup MJXc-space2" id="MJXc-Node-126663"><span class="mjx-base"><span class="mjx-mn" id="MJXc-Node-126664"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" id="MJXc-Node-126665" style=""><span class="mjx-mrow" id="MJXc-Node-126666"><span class="mjx-mn" id="MJXc-Node-126667"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">11</span></span></span></span></span></span><span class="mjx-mtext" id="MJXc-Node-126668"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;"> </span></span><span class="mjx-msubsup" id="MJXc-Node-126669"><span class="mjx-base"><span class="mjx-mtext" id="MJXc-Node-126670"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Nm</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.615em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" id="MJXc-Node-126671" style=""><span class="mjx-mrow" id="MJXc-Node-126672"><span class="mjx-mo" id="MJXc-Node-126673"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn" id="MJXc-Node-126674"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span> ]<br></p> | |