The Rope Question

A long time back a friend had posed this question:

"You have a tennis ball and the earth. You have two ropes. 

One rope ties the tennis ball along its surface. It fits exactly. 

The other rope does the same to the earth,

i.e. exactly covers the circumference of the earth.

You now increase the length of each rope by 1 inch.

Form a circle with each rope covering the tennis ball and the earth
respectively.

Is the distance between the tennis ball and its new circle greater
than that between the earth and its new circle?"

She was looking for the logic and not the Math.

Now since neither my logic nor my Math skills are anything to talk home about, I turned to someone who might have done justice to the problem.


This is the answer I got back:

"Is this a trick question?

If it were, I would ask,

1) What kind of a rope was used, i.e. what was the modulus of elasticity? Did you twist the rope during the process?

2) What was the tension in the rope while it was stretched?

3) What were the temperatures during the experiments?

4) What is the coefficient of thermal expansion, in case there was a temperature variation?

5) How fast was the measurement done? (may become important if we are thinking in speeds near that of the light)

6) The question that has always haunted me since childhood.....how can you tie a knot (to add that 1 inch) without altering the original length?

(That will be close to Heisenberg’s heart too.)

7) Question 6 alone can generate a whole set of debate, like how tight was the knot?

( I won't even get into the uncertainty in measurements!)

8) If you asked my Graduate school advisor he'd ask, "Did you repeat the experiment?"

9) My present boss would ask: "Did you write that up?"

(Just in case you didn't know what writing up is all about, it refers to writing up a US patent)

10) And his boss would suggest," Sign an NDA (non disclosure agreement) before you answer the question!"

11) The Corporate VP would ask, "Can we get the problem solved in China?"

12) Tom Skilling would ask, "Was there a Jet stream in the upper atmosphere pushing the rope?"

13) Dubya Bush would say " Are you sure it is not an act of terrorism?"

14) My Dad who loves a gourmet meal and is a secret poet at heart would ask, " May I hope, to eat the rope?"

15) My health freak brother would say, " Jump the rope 20 min a day to get rid of the extra calories."

16) My sister who is always looking for an excuse to scold me will say, " Who asked you to get in to such a mess with ropes!"

17) My Mom who spent her entire trip to the US trying to find a way to wash and dry her sarees would ask, "Can we dry our laundry on that rope?"

18) And last, my wife who is forever trying to stock up on things will say, " Can we have another rope? Then we can do the experiment with one and keep the other in stock just in case we need it later."

Thanks for asking. Hopefully I answered your question."

Needless to say I was left speechless.

*I'd like to thank AB for the question and AR for sending me the reply.