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 $6 \,m$. 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 this drawing is

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

Answer 1

Answer: (A)

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