Final answer:
The false statement for a cambered airfoil is that the pitching moment at the aerodynamic center is constant with change in angle of attack. While the location of the aerodynamic center and its characteristic of having a constant pitching moment coefficient are correct, the magnitude of the pitching moment itself does vary with angle of attack.
Step-by-step explanation:
The correct answer to the student's question is (d) the pitching moment at the aerodynamic center is constant with change in α (angle of attack). This statement is FALSE for a cambered airfoil. While the aerodynamic center is the point at which all changes in lift force can be said to act, which is generally near the 1/4 chord point at subsonic speeds, the pitching moment is not, in fact, constant with changes in angle of attack. The aerodynamic center is a point where the pitching moment coefficient is constant, not the pitching moment itself. The magnitude of the pitching moment does vary with changes in lift and, therefore, with changes in angle of attack.
It is also important to note that the statement (a) there is no pitching moment at the aerodynamic center is misleading. There is a pitching moment; it is just that its coefficient is constant at the aerodynamic center for small changes in angle of attack.