Final answer:
To measure torque in a system, hanging known masses from a string wound around a spool is the most controlled method, as it allows for predictable and adjustable torque application.
Step-by-step explanation:
The question explores different methods of applying torque to a system and how these methods can be used to study the relationship between torque, angular momentum, and the application time. Method (c), which involves hanging known masses from a string wound around a spool, would allow for a controlled and measurable amount of torque. This is because the gravitational force acting on the known masses would create a predictable torque on the spool, which can be calculated and adjusted for different experiments.