Question

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 centers 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 center of mass of the ink in this drawing is:

• A. $\frac{a}{10}$
• B. $\frac{a}{8}$
• C. $\frac{a}{12}$
• D. $\frac{a}{3}$

Answer 1

The correct option is A $\frac{a}{10}$

$Y_{CM}=\frac{6m\times 0+ma+ma+-ma+m\times 0}{6m+m+m+m+m}$

$Y_{CM}=\frac{ma}{10m}=\frac{a}{10}$