For a uniform square sheet from which another smaller square is cut out as shown in the figure, find out the distance of centre of mass of the remaining part from the y−axis. Consider the origin as shown in figure.
A
1.96cm
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B
16.66cm
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C
36cm
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D
5cm
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Solution
The correct option is B16.66cm Considering the removed smaller square part (side=20cm) as the negative mass superimposed on the larger square (side=40cm)
Area of larger square A1=402 & Area of smaller square A2=202
Their respective x coordinates of COM are given by: x1=20cm & x2=20+10=30cm
The required distance of COM from y axis is the xCM
xCM=A1x1−A2x2A1−A2=((402×20)−(202×30))(402−202)
⇒xCM=503=16.66cm
The cut is symmetric along a line passing through the centre of bigger square and parallel to x− axis, so COM of system will lie along that line. i.e yCM=20cm