Final answer:
The series motor (B) can speed up to dangerously high speeds when loads become very low, due to the direct proportionality of field strength and current in its series configuration.
Step-by-step explanation:
The DC motor that can speed up to dangerously high speeds when loads become very low is the B) series motor. In a series motor, the armature and field coils are connected in series which causes the field strength to be directly proportional to the current. When mechanical load decreases, the current through the motor decreases, and thus the field strength decreases, allowing the motor to speed up. If the load is very low or completely disconnected, the motor could reach destructive speeds due to a lack of back emf to balance the driving emf. This characteristic makes the series motor dangerous when the load can suddenly drop or be entirely lost.
In contrast, shunt motors have their armature and field windings connected in parallel, which maintains field strength even at lower loads, thus avoiding runaway speeds. Squirrel cage motors refer to a type of induction motor which is not a DC motor and therefore not relevant to this context. A compound motor has both series and shunt field windings and is less susceptible to running away than a pure series motor.