Hookes law states that the force required to extend or compress a spring by a certain distance is directly proportional to that distance. Mathematically, it can be expressed as:

F = kx

where F is the force applied to the spring, x is the displacement (extension or compression) of the spring, and k is the spring constant.

Explanation:
According to the given statement, the spring is extended to a length l. It implies that the displacement (x) of the spring is equal to l.

We need to determine the relationship between the force (F) and the displacement (l) based on Hookes law.

Let's substitute x with l in the equation:

F = kl

This implies that the force (F) is directly proportional to the displacement (l). In other words, as the spring is extended to a greater length, the force required to extend it also increases proportionally.

Understanding the Options:
a) F = kl : This is the correct option as it represents the relationship between the force (F) and the displacement (l) according to Hookes law.

b) F = k/l : This option is incorrect as it represents an inverse relationship between force and displacement. Hookes law states a direct relationship.

c) F = k2l : This option is incorrect as it represents a quadratic relationship between force and displacement. Hookes law states a linear relationship.

d) F = k2/l : This option is incorrect as it represents an inverse relationship between force and displacement. Hookes law states a direct relationship.

Conclusion:
The correct answer is option 'A' (F = kl) as it represents the relationship between the force (F) and the displacement (l) according to Hookes law.