A flagpole, \(A B\), is 4 m long. The flagpole is modelled as a non-uniform rod so that, at a distance \(x\) metres from \(A\), the mass per unit length of the flagpole, \(m \mathrm {~kg} \mathrm {~m} ^ { - 1 }\), is given by \(m = 18 - 3 x\).
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The end \(A\) of the flagpole is fixed to a point on a vertical wall. A cable has one end attached to the midpoint of the flagpole and the other end attached to a point on the wall that is vertically above \(A\). The cable is perpendicular to the flagpole. The flagpole and the cable lie in the same vertical plane that is perpendicular to the wall. A small ball of mass 4 kg is attached to the flagpole at \(B\). The cable holds the flagpole and ball in equilibrium, with the flagpole at \(45 ^ { \circ }\) to the wall, as shown in Figure 3.
The tension in the cable is \(T\) newtons.
The cable is modelled as a light inextensible string and the ball is modelled as a particle.
Using the model, find the value of \(T\).
Give a reason why the answer to part (b) is not likely to be the true value of \(T\).