A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion `HBGO` is cut-off, the coordinates of the center of mass of the remaining portion will be:

Options

A. `((5a)/(3),(5b)/(3))`
B. `((5a)/(12),(5b)/(12))`
C. `((2a)/(3),(2b)/(3))`
D. `((3a)/(4),(3b)/(4))`

Answer

B

Explanation

`x = (m(a/4) + m(a/4) + m((3a)/4))/(3m) = (5b)/(12) , " " y = (m(b/4) + m(b/4) + m((3b)/(4)))/(3m) = (5b)/12`.