The outline of a circle is always 2 * Pi * R (R = the radius).
Therefore, the radius will have to decrease by:
100 centimetres / (2 * Pi) =
100 / 6,28 = R = 15,92 cm.
So, to put the cable tightly around the moon the groove should be 15,92 centimetres deep.
Which is still a huge task if you want to gid this deep all around the moon.
The fun thing is, that the depth of the groove does not depend on the radius of the object you are digging it in.
You could as well 'dig a groove' in the globe on your desk: it would still have to be 15,92 centimetres.