Question

Find the position of centre of mass of the uniform planner sheet shown in figure with respect to the origin.

Answer 1

Let us consider a contractile mass $m$ of square $OACE$ of center at point $P$

And a negative mass $(-\frac{m}{4})$ of $BCDP$ of center at $N(\frac{39}{2},\frac{39}{2})$

Now center of mass of $OABPDEO$ is $(x,y)$

$x=\frac{ma-\frac{m}{4}\times \frac{39}{2}}{m-\frac{m}{4}}=\frac{\frac{\frac{5ma}{8}}{3m}}{4}=\frac{5}{6}ay=\frac{5}{6}a(x,y)=(\frac{5}{6}a,\frac{5}{6}a)$