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

Step-by-step solution

Let the initial length of the string be " ? . Tension Elongation of the string aligned T₁ T₂ & = a-l b-l 4 5 = a-l b-l 4 b-4 l & =5 a-5 l l & =5 a-4 b Again, T₁ T₃ & = a-l x-l aligned aligned & x= length of the string at tension T(=9 ~N ) & aligned 4 9 & = a-(5 a-4 b) x-(5 a-4 b) 4 9 & = -4 a+4 b x-(5 a-4 b) 4 9 = 4(-a+b) x-(5 a-4 b) x-(5 a-4 b) & =9 a+9 b x & =-9 a+9 b+5 a-4 b & =5 b-4 a aligned aligned