A uniform inextensible string of length $$L$$ and mass $$M$$ is suspended vertically from a rigid support. A transverse pulse is allowed to propagate down through the string from the support. At the same time, a ball of mass $$m$$ is dropped from the rigid support. The ball will pass the pulse at a distance from the top of the string, that is from the support, equal to

A

$$\frac{15L}{16}$$

B

$$\frac{8L}{9}$$

C

$$\frac{L}{2}$$

D

$$\frac{3L}{4}$$