In the feedback control system shown in the figure, D(s) is step disturbance, R(s) is input and C(s) is output :

The steady-state error component due to a step disturbance for the system is

In the given system, an error will occur due to input R(s) and due to disturbance D(s) error due to disturbance is defined as \(\left. \frac{E(s)}{D(s)}\right|_{R(s) = 0}\)

forward path gain from D(s) to E(s) = \( - \frac{1}{s(s + 40)}\)

∴ \(\left. \frac{E(s)}{D(s)}\right|_{R(s) = 0} = \frac{\frac{-1}{s(s + 40)}}{1 + \frac{10}{s(s + 40)}} = \frac{-1}{s^2 + 40s + 10}\)

∴ E(s) = D(s) × \(\frac{-1}{s^2 + 40s + 10}\)

\(\rm e_{ss} = lt_{s \rightarrow 0} \ s. E(s) = s \times \frac{1}{s} \times \frac{-1}{s^2 + 40s + 10}\)

\(= \frac{-1}{10} = -0.1\)

Therefore, option (a) is correct.