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

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Correct answer: B. 5 b-4 a

Let the initial length of the string be " ? . Tension Elongation of the string aligned (T_1)/(T_2) & =(a-l)/(b-l) (4)/(5)=(a-l)/(b-l) 4 b-4 l & =5 a-5 l l & =5 a-4 b Again, (T_1)/(T_3) & =(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

The length of an elastic string is a metres when the longitudinal...

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