Question

# Five homogeneous bricks, each of length L=9 m are arranged as shown in the figure. Each of the bricks is displaced with respect to the next one in contact by L6 as shown in the figure below. Find the x− coordinate of the centre of mass relative to origin O.

A
2.1 m
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B
5.4 m
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C
4.5 m
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D
6.3 m
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Solution

## The correct option is D 6.3 mGiven length of each brick is L Let the mass of each brick =m kg Initially all five bricks have centre of mass at horizontal distance of L2 relative to origin O. After displacement, the centre of mass of the bricks are given by: x− coordinate of centre of mass of brick 1,x1=L6+L6+L2=5L6 For brick 2,x2=L6+L2=4L6 For brick 3,x3=L2 For brick 4,x4=L6+L2=4L6 For brick 5,x5=L6+L6+L2=5L6 ∴x− coordinate of COM of combined system xCOM=mx1+mx2+mx3+mx4+mx5m+m+m+m+m =m(5L6)+m(4L6)+m(L2)+m(4L6)+m(5L6)m+m+m+m+m =21mL6×5m=21L30 But L=9 m ∴xCOM=21×930=6.3 m

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