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An elastic string has length a m when the longitudinal tension is 4 N and length b m when the longitudinal tension is 5 N. Its length, in metres, when the longitudinal tension is 9 N is

1. a − b
2. 5b − 4a
3. 2b − 1/4 a
4. 4a − 3b

Correct answer: 5b − 4a

Solution

Let L = L0 + kT. Then a = L0 + 4k and b = L0 + 5k, so k = b - a and L0 = 5a - 4b. At T = 9: L = L0 + 9k = (5a - 4b) + 9(b - a) = 5b - 4a.

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