Which component is primarily responsible for controlling the operational state of a motor?

The control relay is primarily responsible for controlling the operational state of a motor because it functions as an electromechanical switch that can open or close circuits in response to input signals. When a control relay receives the appropriate signal, it can energize or de-energize the motor's circuit, facilitating start and stop functions. This control is essential for the automation and coordination of motor operations within various systems.

In contrast, the overload relay is mainly utilized for protecting the motor from overheating due to excess current, and it does not directly control the motor's operational state. The thermal cutout serves a similar protective role by interrupting power to the motor when temperatures exceed safe limits, but it also does not manage the operation of the motor by starting or stopping it. A soft starter gradually ramps up the voltage to the motor during startup to reduce mechanical stress, rather than controlling its overall operational state. Thus, the control relay is integral to initiating and terminating motor operation, making it the correct answer.