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 $6 \mathrm{~m}$. The coordinates of the…

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 $6 \mathrm{~m}$. The coordinates of the centres of the different parts are, outer circle 10 , $0)$, left inner circle $(0,0)$, 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

Aicharya · Accepted Answer

$y_{C M}$ $ \begin{gathered} =\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)}{6 m+m+m+m+m}=\frac{a}{10} \end{gathered} $

Look at the drawing given in the figure, which has been drawn with ink of uniform line-thickness. The mass…

Solution