Question

Five uniform circular plates, each of diameter $b$ and mass $m$, are placed together to form a pattern as shown in the figure. Find the $y$ coordinate of the centre of mass of the system.

• A. $\frac{4b}{5}$
• B. $\frac{b}{3}$
• C. $\frac{b}{5}$
• D. $\frac{2b}{5}$

Answer 1

The correct option is A $\frac{4b}{5}$

Replace the circular plates with point masses placed at their respective $\text{COM}$.
The coordinates of the ${\text{COM}}^{\prime }s$ can be represented as:
$(0,0),(b,0),(0,b),(b,b),(0,2b)$

Applying the formula for $\text{COM}$:

$y_{\text{CM}}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4+m_5{y}_5}{m_1+m_2+m_3+m_4+m_5}$

$=\frac{m\times 0+m\times 0+m\times b+m\times b+m\times 2b}{5m}$

$\therefore y_{\text{CM}}=\frac{4b}{5}$