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Mechanical Properties Of Fluids

Question
CBSEENPH11018902

If an addition of 1250 g tension of string raises its pitch to interval fifth, what is the original tension?

Solution
Interval fifth corresponds to the frequency ratio 3:2.
Let T be the original tension in the string. 
Relation between velocity and tension is given by, 
                              straight v proportional to square root of straight T 
∴                           straight v subscript 2 over straight v subscript 1 equals square root of straight T subscript 2 over straight T subscript 1 end root 
rightwards double arrow                   3 over 2 equals square root of fraction numerator straight T plus 1250 over denominator straight T end fraction end root 
rightwards double arrow                   9 over 4 equals fraction numerator straight T plus 1250 over denominator straight T end fraction 
rightwards double arrow                  space 9 straight T equals 4 straight T plus 5000 
i.e.,                    straight T equals 1000 gm, is the original tension of the string.