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Asked by sarveshvibrantacademy | 18 May, 2019, 13:10: PM
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when the wire is pulled at middle to a distance a, increase in length as shown in figure = PR+RQ
PR+RQ  = begin mathsize 12px style 2 square root of L squared plus a squared end root space equals space 2 L space open parentheses 1 plus a squared over L squared close parentheses to the power of bevelled 1 half end exponent space equals space 2 L space plus space a squared over L space space space w h e n space space a over L less than less than 1 end style
hence change in length ΔL = ( a2/ L )   and strain (ΔL/2L) = ( a2 / 2 L2 ) ....................(1)
 
if Y is youngs modulus, then we have  Y = stress / strain  =  (T/A) / strain ...................(2)
 
where T is tension in wire, A is area of cross section
 
using eqn.(1) and (2), we get T = begin mathsize 12px style fraction numerator a squared space πr squared over denominator 2 L squared end fraction Y end style
Answered by Thiyagarajan K | 18 May, 2019, 16:03: PM

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