The problem states: - Initial head = 60 m - Power developed by turbine = 5 MW - Increase in head = 120 m We need to find the approximate power output when the head is increased to 120 m. --- ### Step-by-step solution: **Power developed by a turbine** is related to the head as: \[ P \propto H^{3/2} \] where \(P\) is power and \(H\) is head. Given: - Initial power \(P_1 = 5\, \text{MW}\) - Initial head \(H_1 = 60\, \text{m}\) - Final head \(H_2 = 120\, \text{m}\) The power at the new head: \[ P_2 = P_1 \times \left(\frac{H_2}{H_1}\right)^{3/2} \] Calculating: \[ \frac{H_2}{H_1} = \frac{120}{60} = 2 \] \[ P_2 = 5 \times 2^{3/2} \] Since: \[ 2^{3/2} = 2^{1 + 1/2} = 2 \times \sqrt{2} \approx 2 \times 1.414 = 2.828 \] Thus: \[ P_2 \approx 5 \times 2.828 = 14.14\, \text{MW} \] --- ### **Correct option:** **14 MW** **Answer: 14 MW**