Question

The coordinates of edges of a square are O(0, 0), A(0, 4), B(4, 4), C(4, 0) respectively, the centre of gravity of square is at coordinates .....

Answer 1

Let $OABC$ is square the centre of mass of sides $OA,AB,BC$ and $CO$ lie on midpoint $M,N,O$ and $Q.$ Then co-ordinate o points are $M(0,2),N(2,4),O(4,2)$ and $Q(2,0)$. Now co-ordinate of the centre of gravity is let $G(x,y)$ mass of all sides of squire is assume$-m.$

$x=\frac{m\times 0+m\times 2+m\times 4+m\times 2}{m+m+m+m}=\frac{8m}{4m}=2y=\frac{m\times 2+m\times 4+m\times 2+m\times 0}{4m}=\frac{8m}{4m}=2$

So,$G(2,2)$ is center of gravity that is point $p(2,2)$