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 ink used to draw the outer circle is 6$m$. 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 the drawing is [image:7_image48.emf]

Question

Dr. Abubacker · Accepted Answer

(a) $y_{CM} = \ \frac{m_{1}y_{1} + m_{2}y_{2} + m_{3}y_{3} + m_{4}y_{4} + m_{5}y_{5}}{m_{1} + m_{2} + m_{3} + m_{4} + m_{5}}$
$= \frac{(6m)(0) + m(a) + m(a) + m(0) + m( - a)}{6m + m + m + m + m} = \frac{a}{10}$

Explanation

Reviewed by Dr. Abubacker

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