# A square of side 4 cm and uniform thickness is divided into four equal square if one of the square is cut off , find thel position of the center of mass of the remaining portion from O

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by sahil12

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by sahil12

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Let us say ABCD is the square with each side = 2 * a. Let O be the center of the square with origin at the center O. We divide the big square into four small squares with one in each quadrant. Each square has a side = a.

Let the mass of the square ABCD be = 4 * M. Then each small square has a mass = M = a². Let us omit one small square in the 3rd quadrant. There remain 3 of them now.

The center of mass of each small square is at its center. So the centers of masses of the three small squares are at :

(- a/2, a/2) , (a/2, - a/2) and (a/2, a/2)

x coordinate of the center of mass:

x = [ M (-a/2) + M (a/2) + M (a/2) ]/ (3 M)

x = a/6

y coordinate of the center of mass

y = [ M (a/2) + M (-a/2) + M (a/2) ]

y = a/6

So CM is at (a/6, a/6) from the center of the big square.

Let the mass of the square ABCD be = 4 * M. Then each small square has a mass = M = a². Let us omit one small square in the 3rd quadrant. There remain 3 of them now.

The center of mass of each small square is at its center. So the centers of masses of the three small squares are at :

(- a/2, a/2) , (a/2, - a/2) and (a/2, a/2)

x coordinate of the center of mass:

x = [ M (-a/2) + M (a/2) + M (a/2) ]/ (3 M)

x = a/6

y coordinate of the center of mass

y = [ M (a/2) + M (-a/2) + M (a/2) ]

y = a/6

So CM is at (a/6, a/6) from the center of the big square.