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anonymous
 5 years ago
1. A square tile of side 2x mm and thickness y mm rests on a horizontal platform. A second tile of the same type is placed over the first so that only one side of the second protrudes over a parallel side of the first by r mm. A third tile is placed over the second so that only one side of the third protrudes over a parallel side of the second by r mm. A fourth is placed over the third in a similar way and so on. (Crosssection of the tiles is shown below.)




Assume that the centre of gravity of each tile is at the centre of the tile. If
anonymous
 5 years ago
1. A square tile of side 2x mm and thickness y mm rests on a horizontal platform. A second tile of the same type is placed over the first so that only one side of the second protrudes over a parallel side of the first by r mm. A third tile is placed over the second so that only one side of the third protrudes over a parallel side of the second by r mm. A fourth is placed over the third in a similar way and so on. (Crosssection of the tiles is shown below.)     Assume that the centre of gravity of each tile is at the centre of the tile. If

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0A is the lowest corner of the first tile, denote the horizontal distance of the centre of gravity of the kth tile by xk, so that x1 = x, x2 = x+r, x3 = x + 2r, . . . The centre of gravity of n slabs placed in the above manner is at a horizontal distance x from A given by x = (x1 + x2 + . . . xn)/n. The nth slab will topple over if x > AB = 2x. (a) Write down an explicit expression for x in terms of x, r and n. (b) Find the maximum number of slabs that can be so placed without toppling over in the following cases. (i) x = 50, r = 5. (ii) x = 50, r = 8. (iii) General case of x, n.
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