Breaking Bricks!!!!!
A chimney on the top of the house was standing intially at the top of a house.
Suddenly it topples. If the width and length of the chimney is less as compared to its height, where it is most likely to break when it falls down ? (Tell at what height from the base it would break) The height of chimney is 09 inches.
Give the answer to its nearest integer value ?
The answer is 3.
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A nice david Morin problem,
The big way is to assume that the cylinder is made of stacks , which have a small but finite thickness and deal with it,
The better and cheaper way is what i did, simple found the tension assuming its a rod that is pivoted at base and falling down, found out the tension as a function of distance from base (i used condition of static equillibrium in rotating frame and conservation of energy for this)
then found out where the tension is maximum as function of angle it rotates
from hindsight concluded that the chimney is most likely to break just before falling (as the break is due to rotation , and angular speed is maximum just before falling) and put theta pi/2 to get l/3
it is interesting to note that the rod is likely to break at infinity when angle with vertical (call it x) is 0 which means it wont break at that instant at all which is perfectly reasonable , and that break point gradually receeds from infinity to l/3 by the time the rod is just about to fall, or x= pi/2 which however becomes obvious only when conservation of energy comes into play,,
I shall post solution if needed by anyone,,,