Question

A square of side `4 m` having uniform thickness is divided into four equal squares as shown in Fig. If one of the squares is cut off, find

the position of centre of mass of the remaining portion from the centre `O`.

Answer 1

Let `m` be the mass of each small square. Therefore, total mass of given square `= 4m`. This acts at the centre `O` of the square. Let `O_(1)` be cm of the cut off square (shown shaded) of mass `m and O_(2)` be cm of the remaining square of mass `3m`.
Now, `AC = sqrt(AB^(2) + BC^(2)) = sqrt(4^(2) + 4^(2)) = 4sqrt(2) cm`
`OC = (1)/(2)AC = (4sqrt(2))/(2) = 2sqrt(2) cm`
`OO_(1) =(1)/(2) = sqrt(2) cm`
Now, moment of unshaded portion of mass `(3 m)` about` O =` moment of shaded portion of mass `(m)` about `O`.
`:. 3m xx OO_(2) = m xx OO_(1)`
`OO_(2) = (1)/(3) (OO_(1)) = (1)/(3) xx sqrt(2) cm`