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CBSE Class 11-science Answered

The length of a metal wire is L when tension in it is T and l when the tension in it is t. Find the original length of the wire
Asked by ZIA HAIDER | 10 Nov, 2014, 06:39: PM
answered-by-expert Expert Answer
Let l0 be the original length of the wire and A be the area of cross section of the metal wire.
In the first case:
Length of the wire is L, when tension in it is T
so change in length,Δlo in this case is  (L - l0)
In the second case:
Length of the wire is l when tension in it is t
so change in length,Δl0 in this case is (l - l0)
begin mathsize 14px style We space know space that space young apostrophe straight s space modulus space of space elasticity comma space straight Y space equals fraction numerator Normal space stress over denominator Longitudinal space strain end fraction Normal space stress space equals straight F over straight A equals straight T over straight A Longitudinal space strain space equals fraction numerator increment straight l over denominator straight l end fraction comma space here space fraction numerator increment straight l subscript 0 over denominator straight l subscript 0 end fraction left parenthesis as space the space original space length space in space this space case space is space straight l subscript 0 right parenthesis So space we space can space write space comma space straight Y space equals space straight T over straight A cross times fraction numerator straight l subscript 0 over denominator increment straight l subscript 0 end fraction First space case : straight Y space equals straight T over straight A cross times fraction numerator straight l subscript 0 over denominator open parentheses straight L minus straight l subscript 0 close parentheses end fraction Second space case space : straight Y space equals space straight t over straight A cross times fraction numerator straight l subscript 0 over denominator open parentheses straight l minus straight l subscript 0 close parentheses end fraction So : straight T over straight A cross times fraction numerator straight l subscript 0 over denominator open parentheses straight L minus straight l subscript 0 close parentheses end fraction equals straight t over straight A cross times fraction numerator straight l subscript 0 over denominator open parentheses straight l minus straight l subscript 0 close parentheses end fraction straight T open parentheses straight l minus straight l subscript 0 close parentheses equals straight t open parentheses straight L minus straight l subscript 0 close parentheses Tl space minus Tl subscript 0 equals tL minus tl subscript 0 straight l subscript 0 left parenthesis straight t minus straight T right parenthesis space equals tL space minus Tl straight l subscript 0 equals fraction numerator open parentheses tL space minus Tl close parentheses over denominator left parenthesis straight t minus straight T right parenthesis end fraction bold Therefore bold space bold the bold space bold original bold space bold length bold space bold of bold space bold the bold space bold wire bold comma bold space bold l subscript bold 0 bold space bold equals fraction numerator open parentheses bold tL bold space bold minus bold Tl close parentheses over denominator bold left parenthesis bold t bold minus bold T bold right parenthesis end fraction end style 
Answered by Jyothi Nair | 11 Nov, 2014, 08:55: AM

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