Question 301: Centre of Mass and Rotational Motion

Question

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

Accepted Answer

The center of mass of each rod is located at its midpoint. The rods can be treated as point masses positioned at their respective centres of mass.
$$ \begin{aligned} X_{c m} & =\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3} \ & =\frac{m(0)+m(a)+m(a)}{3 m} \ & =\frac{2 a}{3} \ Y_{c m} & =\frac{m_1 y_1+m_2 y_2+m_3 y_3}{m_1+m_2+m_3} \ & =\frac{m\left(\frac{a}{2}ight)+m\left(\frac{a}{2}ight)+m(0)}{3 m}=\frac{a}{3} \end{aligned} $$

Answer

$\left(\frac{\mathrm{a}}{3}, \frac{\mathrm{a}}{3}\right)$

Answer

$\left(a, \frac{a}{2}\right)$

Answer

$\left(2 a \frac{a}{2}\right)$

Answer

$\left(\frac{2 a}{3}, \frac{a}{3}\right)$

Centre of Mass and Rotational Motion

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

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