Question

Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the shown, find the y co-ordinate of the center of mass of the five plate system.

Answer 1

$\large{\underline{\sf{Solution:-} }}$

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Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the shown, find the y co-ordinate of the center of mass of the five plate system.

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Replace the circular plates with point masses placed at their respective $\displaystyle{COM.}$

The coordinates of the $\displaystyle{COM′s}$ can be represented as:

$\sf {(0, 0), (b, 0), (0, b), (b, b), (0, 2b)}$

Apply the formula of COM:-

$\rm{yCM = \dfrac{m_1y_1 + m_2y_2 + m_3y_3 + m_4y_4 + m_5y_5}{m_1 + m_2 + m_3 + m_4 + m_5}}$

$\rm\leadsto{\dfrac{m × 0 + m × 0 + m × b + m × b + m × 2b}{5m}}$

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