Physics 205, Physics 215, Astronomy 211 - Assume the moon is a perfect sphere. Somebody puts a rope tightly around the equator of the moon so that no space is left between the rope and the moon's surface. Then he cuts the rope, inserts 1 m of rope between the two ends of the cut rope, and redistributes the rope around the equator so that it has an equal distance everywhere from the surface of the moon.
The distance between the rope and the moon now is
(a) enough for a cat to squeeze through under the rope
(b) just barely enough for a mouse to squeeze through under the rope
(c) not nearly enough for a mouse to squeeze through
(d) impossible to say without knowing the moon's diameter.
Answer. Choice (a) is the correct one.
Explanation. The distance between the rope and the moon, after 1 m has been inserted, is independent of the radius of the moon. We will now calculate this distance and see that the moon's radius drops out of the calculation.
Let us define the following symbols:
R = radius of moon, r = radius of rope (with 1 m inserted)
C = circumference of moon, c = circumference of rope.
Doing the calculation in SI-units, we have c = C + 1. Since the radius of a circle is equal to the circumference divided by 2 pi, (pi = 3.14...), we get
r = c/(2 pi) = (C + 1)/(2 pi) = C/(2 pi) + 1/(2 pi)
= R + 1/6.28 m.
Thus, the rope is 1/6.28 m above the moon's surface. This is approximately 16 cm, easily enough space for a cat to squeeze through.