In the tower of a church, two bell ropes pass through small holes a foot apart in a high ceiling and hang down to the floor of a room. A skilled acrobat, carrying a knife and bent on stealing as much of the two ropes as possible, finds that the stairway leading above the ceiling is barred by a locked door.
There are no ladders or other objects on which he can stand and so he must accomplish his theft by climbing the ropes hand over hand and cutting them at points as high as possible. The ceiling is so high, however, that a fall from even one-third the height could be fatal. By what procedure can he obtain a maximum amount of rope?
And while we’re absolutely not on the same subject at all let me say that I’ve had a massively huge grand total of TWO (yes, the same number that comes after ONE) answers (and one of them is not even remotely correct) to the problem of what happens if while travelling forwards at 10,000 kmph you shoot yourself with a bullet travelling backwards towards your forehead at the same speed.
To help you picture this: you’re holding a Smith & Wesson or Colt or Uzi machine pistol or whatever and want to commit space suicide. Can you do it? Want to try this problem again or keep shooting down the easy ones as usual?
(The problem was about two each of red, green and yellow balls and for each colour one ball is heavy and one light which weigh the same respectively.
And of course there’s this beam balance. You figure out the rest.) This is a fascinating problem. The answer is the heavier balls can be determined in two weighings. Let us call the balls R1, R2, G1, G2 and Y1 Y2. Scenario 1:Weigh R1G1 against R2Y1; (a). If equal, weigh R1 and G1, if R1 is heavier G1 is lighter. Consequently we can determine that R1, G2 and Y1 are heavier and R2, G1 and Y2 are lighter. Scenario 2: R1G1 is lighter than R2Y1.
Now weigh G2 against Y2. If G2 happens to be heavier than Y2, we can conclude that G1 is lighter than Y2. This gives R2, Y1and G2 as the heavier balls. If G2 is lighter than Y2, Y1 is also lighter than G1. In this case also R2 has to be heavy. Therefore R2, G1 and Y1 are the heavier balls. -- Gopunatarajan Natarajan, natarajangopunatarajan3@gmail. com
(The other problem was: “Push an empty steel drum into the ocean. Is it possible that when pushed down far enough it just floats or sinks? If so what happens to the energy of the work done pushing it down?”) As the empty drum is pushed down inverted into the ocean floor, work is done against the buoyancy force leading to compressing the air within. At a certain depth, air would have compressed to such a density equal to density of water at that depth.
Thus, buoyancy force becomes zero, which means the inverted drum will just stay there (provided the drum has the capacity to hold that pressure). -- Rekha G, g. email@example.com (That’s absolutely bang on RG but the additional question was:
“If so what happens to the energy of the work being done pushing it down?” -- MS) The energy or the work done in pushing the drum down into the ocean will result in slightly increasing the temperature of the water due to compression of the water.
– K Narayana Murty, firstname.lastname@example.org The work done in pushing the drum down is stored as potential energy of the compressed air which is equal to the product of the pressure exerted and the change in volume. -- Balagopalan Nair K, email@example.com
The energy is stored as potential energy in the air inside the drum which gets progressively compressed as the drum is pushed down and starts acting just like a coiled spring. Where’s the problem here? -- Dhruv Narayan, firstname.lastname@example.org
BUT GOOGLE THIS NOW
1. Consider the sum of the series : 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 . . . .
After how many terms can we be certain that the sum exceeds 100. Or can we ever?
2. Two identical cars collide head on.
Each car is travelling at 100 kmph. The impact force on each car is the same as hitting a solid wall at what speed? (And of course since it goes without saying even when it’s said, why?)
Sharma is a scriptwriter and former editor of Science Today magazine. (email@example.com)