A square of side `2cm` and uniform thickness is divided into four squares. The square portion `A^'AB^'D` is removed and the removed portion is placed over the portion `DB^'BC^'`. The new position of centre of mass is

Options

A. `(2cm, 2cm)`
B. `(2 cm, 3cm)`
C. `(2cm, 2.5cm)`
D. `(3cm, 3cm)`

Answer

C

Explanation

`x_(CM)=(A_1x_1+A_2x_2+A_3x_3+A_4x_4)/(A_1+A_2+A_3+A_4)`
`=((4)(1)+(4)(1)+(4)(3)+(4)(3))/(16)=2cm`
`y_(CM)=(A_1y_1+A_2y_2+A_3y_3+A_4y_4)/(A_1+A_2+A_3+A_4)`
`=((4)(1)+4(3)+4(3)+4(3))/(16)=2.5cm`