The length of an elastic string is a metre when the longitudinal tension is 4 ~N and b metre when the longitudinal tension is 5 ~N . The length of the string in metre when longitudinal tension is 9 ~N is

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Correct answer: B. 5 b-4 a

Let L is the original length of the wire and k is force constant of wire. Final length = initial length + elongation L^ =L+ (F)/(k) For first condition a=L+(4)/(k) For second condition b=L+(5)/(k) By solving Eqs. (i) and (ii), we get L=5 a-4 b and k= (1)/(b-a) Now, when the longitudinal tension is 9 ~N , length of the string array l =L+(9)/(k)=5 a-4 b+9(b-a) =5 b-4 a array

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