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

Let l be the natural length and k =YAlbe the forceconstant of wire. Then,a=l+4k   … (i) ∵F=kΔl or Δl=Fkand   b=l+5k                       …(ii)On solving Eqs. (i) and (ii), we get or  1k=(b−a) and l=(5a−4b)Now, when T = 9Nl'=l+9k=(5a−4b)+9(b−a)=(5b−4a)