The force constant k of a spring is a measure of how stiff or soft the spring is. It quantifies the relationship between the force applied to the spring and the displacement produced.

Option 1: N-m. This unit represents torque, which is a measure of how a force causes rotation. It is not the appropriate unit for the force constant of a spring.

Option 2: N/m. This is the correct unit for the force constant of a spring. It represents the force required to stretch or compress the spring by a unit length.

Option 3: N-m^2. This unit represents the second moment of force, which is a measure of how a force causes bending or twisting. It is not the appropriate unit for the force constant of a spring.

Option 4: N/m^2. This unit represents pressure or stress, which is a measure of force per unit area. It is not the appropriate unit for the force constant of a spring.

Therefore, the correct unit for the force constant k of a spring is option 2: N/m.