Men on the Moon
The moon's diameter is not needed to solve this problem!
Let the moon's radius be r meters.
Then the length of the cable is 2×pi×r-1 meters.
Let the depth of the groove be x meters.
2×pi×(r-x) must be equal to 2×pi×r-1.
Solving the equation 2×pi×(r-x)=2×pi×r-1 gives x = 1/(2×pi) meters (about 0.159 meters).
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