Which condition will prevent the nose gear from extending in a hydraulic system?

The correct answer relates to the operational dependencies of the hydraulic systems that control the landing gear extension mechanisms. In the CRJ550, the nose gear extension is primarily supported by hydraulic system 2, which provides the necessary pressure to actuate the gear.

When there is a loss of hydraulic system 2, the system that directly affects the nose gear's ability to extend is compromised. Additionally, hydraulic system 3 has a cross-tie capability with hydraulic system 2, meaning that it can provide supplementary pressure if necessary. Therefore, a loss of both hydraulic system 2 and system 3 would indeed prevent the nose gear from extending due to the direct loss of hydraulic pressure required for the gear's operation.

This understanding highlights the importance of hydraulic systems in aircraft operation, particularly regarding safety-critical systems like landing gear. The other hydraulic systems may support other functions, but in this specific case, the failure of systems 2 and 3 creates a scenario in which the nose gear cannot be extended.