# Extensible string on a pulley

Suppose we have an extensible massless string satisfying Hooke's Law, tied to a wall at one end and going over a 'fricional pulley'. Now if we tie the other end with a mass 'M', the total length of the string changes by ΔL and the pulley rotates by angle θ. I came across that ΔL=Rθ, which I couldn't understand. I know that the point A (on the string) will move anticlockwise w.r.t. the pulley and point B clockwise. Can anyone find how ΔL and θ are related?

$$s = r\theta$$
for small angular displacements, where $$s$$ is the arc length, $$\theta$$ is the angle and $$r$$ is the radius of the circle.