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) = (6m xx 0 + m xx a + m xx a + m xx 0 + m xx (-a))/(10 m)`
`Y_(CM) = a/10`