JEE Advance - Physics (2009 - Paper 1 Offline - No. 2)
Look at the drawing given in the figure below 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
Explanation
The coordinates of centre of mass is defined as
$${R_{CM}} = {{\sum\nolimits_i {{m_i}{r_i}} } \over {\sum\nolimits_i {{m_i}} }}$$
Thus,
$${Y_{CM}} = {{(6m \times 0) + (m \times a) + (m \times a) + (m \times 0) + (m \times - a)} \over {6m + m + m + m + m}} = {a \over {10}}$$
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