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 the longitudinal tension is 9 N is

Let L be the original length of the wire and K be the force constant of wire.Final length = Initial length + ElongationL′=L+FKFor first condition a=L+4K  ……(i)For second condition b=L+5K ……..(ii)By solving equations (i) and (ii), we getL=5a−4b and K=1b−aNow when the longitudinal tension is 9 N, length of the string=L+9K=5a−4b+9(b−a)=5b−4a