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A square of side 4 cm and of uniform thi...

A square of side 4 cm and of uniform thickness is divided into four equal squares. If one of them is cut off (OECF), then the position of the centre of mass of the remaining portion from O is `(sqrt2)/k cm` . Find the value of K.

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3
Let `sigma` be surface mass density. The mass of the removed portion may be taken as negative. The given system may be regarded as two-particle system—one particle of mass `16 sigma` at (0, 0) and second particle of mass `'-4 sigma'` at (1 , -1).
Now, `x = (16 sigma xx 0 - 4 sigma (1))/(12 sigma) = -1/3 cm and y = (16 sigma xx 0 - 4 sigma(-1))/(12 sigma) = 1/3 cm`
`r = sqrt((-1/3)^2 + (1/3)^(2)) cm = (sqrt2)/3 cm`.
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