Question

Figure shows a composite system of two uniform rods of lengths as indicated. Then the coordinates of the centre of mass of the system of rods are

• A. $\left(\frac{L}{2}, \frac{2 L}{3}\right)$
• B. $\left(\frac{L}{4}, \frac{2 L}{3}\right)$
• C. $\left(\frac{L}{6}, \frac{2 L}{3}\right)$
• D. $\left(\frac{L}{6}, \frac{L}{3}\right)$

Answer 1

Answer: (C)

Centre of mass of the uniform rod will lie at its centre
$x_{ cm }=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}}$
$x_{ cm }=\frac{m\left(\frac{L}{2}\right)+2 m(0)}{3 m}, y_{c m}=\frac{2 m(L)+m(0)}{3 m}$
$x_{ cm }=\frac{L}{6}, y_{ cm }=\frac{2 L}{3}$