When the mechanical power is developed by a DC motor, the back electromotive force (EMF) is equal to half of the applied voltage.

In a DC motor, the back EMF is generated due to the rotation of the armature in the magnetic field created by the field winding. The back EMF opposes the applied voltage and is directly proportional to the speed of the motor. As the motor speed increases, the back EMF also increases.

At maximum mechanical power output, the motor operates at its maximum efficiency point, which occurs when the input electrical power is equal to the output mechanical power. At this point, the back EMF is equal to half of the applied voltage. This is because the voltage drop across the armature resistance is equal to the remaining half of the applied voltage, resulting in maximum power transfer.

Therefore, the correct answer is B: Back EMF is equal to half of the applied voltage.