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A square plate of edge $$a cm$$ if the areal density at $$P$$ is $$k x$$ g/cm $${ } ^ { 2 }$$ , where $$x$$ is the distance from $$P$$ to one edge of the square
$$m = \frac { k a ^ { 3 } } { 2 } ; \quad \overline { x } = \frac { 2 a } { 3 } , \quad \overline { y } = \frac { a } { 2 }$$