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A brick of length L is placed on the horizontal floor.The bricks of same length and size are placed on this brick,on above the other by providing a margin a margin of L/8 from the edge of the brick placed just below,in the same direction.Find the correct option.
a.fifth brick will fall down
b.sixth brick alone will fall down
c.sixth brick along with fifth brick will fall down
d.fifth brick along with fourth brick will fall down
let CoM of first brick be origin(0,0), and let all the brick lengths lie along x-axis. CoM of first two bricks=(L/16,0),first three bricks=((L/4)+2(L/16))/3 =(L/8,0), first four bricks=((3L/8)+3(L/8))/4=(3L/16,0),first five bricks=((4L/8)+4(3L/16))/5=(4L/16,0), first six bricks=((5L/8)+5(4L/16))/6=5L/16,now let us consider CoM of each brick individually.second brick=(L/8,0), third brick=2L/8, fourth=3L/8,fifth=4L/8=L/2,thus the fifth brick lies exactly on the line dividing falling and not falling, but being on the line itself as is the case barely ensures that the first five bricks are stable.Now, if a sixth brick is added, it is clear that first of all the sixth brick considered alone will fall down.In addition,fifth brick, which lies exactly at the borderline, will be tipped over by the falling sixth brick. Therefore,sixth brick along with fifth brick will fall down.
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