Qstnid -Ii-4-two Wires A And B Are Made Of Same Material. The Wire A Has A Length L And Diameter R While The Wire B Has A Length 2l And Diameter R/2. If The Two Wires Are Stretched By The Same Force, The Elongation In A Divided By The Elongation In B Is - 14: Some Mechanical Properties Of Matter

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NEET-XII-Physics

14: Some Mechanical Properties of Matter

with Solutions - page 2

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#4
Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
(a) 1/8
(b) 1/4
(c) 4
(d) 8
digAnsr: a
Ans : (a) 1/8
`` \,\mathrm{\,Suppose\,}\,\mathrm{\,the\,}\,\mathrm{\,Young\,}\text{'}\,\mathrm{\,s\,}\,\mathrm{\,modulus\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,wire\,}\text{'}\,\mathrm{\,s\,}\,\mathrm{\,material\,}\,\mathrm{\,be\,}\,\mathrm{\,Y\,}.``
`` \,\mathrm{\,Here\,}:``
`` \,\mathrm{\,Force\,}=\,\mathrm{\,F\,}``
`` {\,\mathrm{\,A\,}}_{1}={\,\mathrm{\,\pi r\,}}^{2}``
`` {\,\mathrm{\,L\,}}_{1}=\,\mathrm{\,l\,}``
`` {\,\mathrm{\,A\,}}_{2}=\,\mathrm{\,\pi \,}{\left(\frac{\,\mathrm{\,r\,}}{2}\right)}^{2}=\frac{{\,\mathrm{\,\pi r\,}}^{2}}{4}``
`` {\,\mathrm{\,L\,}}_{2}=2\,\mathrm{\,l\,}``
`` \,\mathrm{\,Suppose\,}\,\mathrm{\,the\,}\,\mathrm{\,elongation\,}\,\mathrm{\,in\,}\,\mathrm{\,A\,}\,\mathrm{\,be\,}\,\mathrm{\,x\,}\,\mathrm{\,and\,}\,\mathrm{\,that\,}\,\mathrm{\,in\,}\,\mathrm{\,B\,}\,\mathrm{\,be\,}\,\mathrm{\,y\,}.``
`` ``
`` \,\mathrm{\,Since\,}\,\mathrm{\,the\,}\,\mathrm{\,Young\,}\text{'}\,\mathrm{\,s\,}\,\mathrm{\,modulus\,}\,\mathrm{\,for\,}\,\mathrm{\,both\,}\,\mathrm{\,the\,}\,\mathrm{\,wires\,}\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,same\,}:``
`` \,\mathrm{\,Y\,}=\frac{{\displaystyle \raisebox{1ex}{$\,\mathrm{\,F\,}$}\!\left/ \!\raisebox{-1ex}{${\,\mathrm{\,A\,}}_{1}$}\right.}}{{\displaystyle \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$l$}\right.}}=\frac{{\displaystyle \raisebox{1ex}{$\,\mathrm{\,F\,}$}\!\left/ \!\raisebox{-1ex}{${\,\mathrm{\,A\,}}_{2}$}\right.}}{{\displaystyle \raisebox{1ex}{$\,\mathrm{\,y\,}$}\!\left/ \!\raisebox{-1ex}{$2\,\mathrm{\,l\,}$}\right.}}``
`` \Rightarrow \frac{\,\mathrm{\,x\,}}{\,\mathrm{\,y\,}}=\frac{{\,\mathrm{\,A\,}}_{2}}{2{\,\mathrm{\,A\,}}_{1}}``
`` \Rightarrow \frac{\,\mathrm{\,x\,}}{\,\mathrm{\,y\,}}=\frac{1}{8}``
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