Question

A square of side A 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:

• A. $\frac{1}{\sqrt{3}}cm$
• B. $\frac{2}{\sqrt{3}}cm$
• C. $\frac{5}{\sqrt{3}}cm$
• D. $\frac{\sqrt{2}}{3}cm$

Answer 1

The correct option is D $\frac{\sqrt{2}}{3}cm$

$x_{em}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m}$
$o=3m_2{x}_1+m_2{x}_2$
$x_2=-3x_1$
Similarly $y=-3y_1$
$(x_2,y_2)=(\frac{A}{y},\frac{-A}{y})$
$(x_1,y_1)=(\frac{-A}{12},\frac{A}{12})$
$\frac{A}{12}\sqrt{2}=\frac{\sqrt{2}}{3}cm(ifA=y)$