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

Step-by-step solution

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