Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is `m`. The mass of the ink used to draw the outer circle is `6m`.
The coordinates of the centres of the different parts are: outer circle `(0, 0)`, left inner circle `(-a, a)`, right inner circle `(a, a)`, vertical line `(0, 0)` and horizontal line `(0, -a)`. The `y`-coordinate of the centre of mass of the ink in this drawing is

Options

A. `(a)/(10)`
B. `(a)/(8)`
C. `(a)/(12)`
D. `(a)/(3)`

Answer

A

Explanation

`Y_(cm) = (m_(1)y_(1) + m_(2)y_(2) + m_(3)y_(3))/(M_(1) + M_(2) + M_(3))`
`Y_(cm) = (6m(o) + m( + a) + m(a) + m(-a) + m(0))/(10m), Y_(cm) = (a)/(10)`