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Question

Four homogeneous brick, each of length L=4 m, are arranged as shown in the figure. Each brick is displaced with respect to one in contact by L8. Find the x coordinate of centre of mass relative to origin O



Your Answer
A
2.5 m
Your Answer
B
1.75 m
Your Answer
C
2 m
Correct Answer
D
2.75 m

Solution

The correct option is D 2.75 m
length of each brick, L=4 m, Let the mass of each brick be m kg.

Initially all four bricks have their COM at L2=2 m from the xaxis. 


After displacing the bricks, coordinates relative to origin O :
x coordinate of COM of brick (1)x1=L2
x coordinate of COM of brick (2)x2=L2+L8=58L
x coordinate of COM of brick (3)x3=L2+L8+L8=68L
x coordinate of COM of brick (4)x4=L2+L8+L8+L8+78L
Replacing the bricks by point masses placed at their COM , the x coordinate of COM of system:

xCM=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4
xCM=m(L2)+m(5L8)+m(6L8)+m(7L8)m+m+m+m
xCM=2232L
xCM=2232×4=228=2.75 m

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