A 2.00-m by 4.00-m uniform sheet of plywood is in a coordinate system with the o

Question

A 2.00-m by 4.00-m uniform sheet of plywood is in a coordinate system with the origin at its center, the x-axis along the longer dimension of the sheet is positive to the right and the y-axis along the shorter dimension is positive upwards. The section of the plywood in the 3rd quadrant is sawed off and the resulting piece is then glued squarely over the 4th quadrant portion of the plywood with glue of negligible weight.What are the x- and y-coordinates of the resulting center of gravity for this arrangement?

a) (0.50 m, 0 m)

b) (1.0 m, 0 m)

c) (1.0 m, -0.50 m)

d) (0 m, 1.0 m)

Explanation / Answer

Let total mass of rectangle = 4m

Initial center of gravity was at (0,0)

Center of gravity of one part in 2nd and one part in 4th quadrant is at (0,0) total mass = 2m

Now center of gravity of one part in 1st quadrant and another glued part in 4th quadrant is at (1,0), mass = 2m

Since same masses have COG at (0,0) and (1,0),

effective COG of total shape = (0.5,0)

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