b
(b) Let \(L\) is the original length of the wire and \(K\) is force constant of wire.

Final length \(=\) initial length \(+\) elongation

\(L' = L + \frac{F}{K}\)

For first condition \(a = L + \frac{4}{K}\)…\((i)\)

For second condition \(b = L + \frac{5}{K}\)…\((ii)\)

By solving \((i)\) and \((ii)\) equation we get

\(L = 5a - 4b\) and \(K = \frac{1}{{b - a}}\)

Now when the longitudinal tension is \(9N,\)

length of the string \(=\) \(L + \frac{9}{K}\)= \(5a - 4b + 9(b - a)\)\(x = 5b - 4a\).