First slide

Centre of mass(com)

Question

The 'y' coordinate of the center of mass of the system of three rods of length '2a' and two rods of length 'a' as shown in the figure is:
(Assume all rods to be of uniform density)

Moderate

A

$\frac{9 a}{8 \sqrt{3}}$
B

$\frac{9 a}{16 \sqrt{3}}$
C

$zero$
D

$\frac{8 a}{\sqrt{3}}$

Solution

The y-coordinate of center of mass is
$\begin{array}{l} y_{c m} = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3} + m_{4} y_{4} + m_{5} y_{5}}{m_{1} + m_{2} + m_{3} + m_{4} + m_{5}} \\ = \frac{2 m (\frac{\sqrt{3}}{2} a) + 2 m (0) + 2 m (0) + m (\frac{\sqrt{3}}{4} a) + m (\frac{\sqrt{3}}{4} a)}{8 m} \\ = \frac{9 a}{16 \sqrt{3}} \end{array}$

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