Question

A uniform square of side $2l$ is divided into four squares. If one them is cut off (represented by shaded region in figure) then the position of centre of mass of the remaining portion from the origin is

• A. $(\frac{7L}{6},\frac{5L}{6})$
• B. $(\frac{L}{6},\frac{L}{6})$
• C. $(\frac{L}{2},\frac{L}{2})$
• D. $(\frac{5L}{6},\frac{7L}{6})$

Answer 1

The correct option is D $(\frac{5L}{6},\frac{7L}{6})$

Let $\sigma$ = mass per unit square unit of square mass of full square $\left(M\right)=\sigma (2l{)}^2=4\sigma l^2$ mass of cut off square $\left(M^{\prime }\right)=\sigma l^2$
$x_{cm}=\frac{Ml+(-M^{\prime })\frac{3l}{2}}{M+(-M^{\prime })}=\frac{4\sigma l^3+(-\sigma l^3)\left(\frac{3l}{2}\right)}{4\sigma l^2+(-\sigma l^2)}=\frac{5l}{6}$
$y_{cm}=\frac{Ml+(-M^{\prime })\left(\frac{l}{2}\right)}{M+(-M^{\prime })}=\frac{7l}{6}$