A square of side `a` and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.
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Options

A. `((5)/(12)a, (5)/(12)a)`
B. `((7)/(12)a, (7)/(12)a)`
C. `((1)/(4)a, (1)/(4)a)`
D. `((1)/(3)a, (1)/(3)a)`

Answer

A

Explanation

(a) Let mass of each is `m`. Coordinates of their respective centre of masses are shown in figure.
`x_(cm) = (m (a)/(4) + m(3a)/(4) + m(a)/(4))/(m + m + m) = (5a)/(12)`
`x_(cm) = (m (a)/(4) + m(a)/(4) + m(3a)/(4))/(m + m + m) = (5a)/(12)`.
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