Centre of mass of two thin uniform rods of same length but made up of different materials & kept

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Centre of mass of two thin uniform rods of same length but made up of different materials & kept as shown, can be, if the meeting point is the origin of co-ordinates

Accepted Answer

Sol.$x_{cm} = \frac{m_{1}.\frac{L}{2}}{m_{1} + m_{2}} = \frac{(\lambda_{1}.L).{L/}2}{(\lambda_{1}.L + \lambda_{2}L)} = \left( \frac{\lambda_{1}}{\lambda_{1} + \lambda_{2}} \right).\frac{L}{2}$$y_{cm} = \frac{m_{2}.\frac{L}{2}}{m_{1} + m_{2}} = \left( \frac{\lambda_{2}.L}{\lambda_{1}.L + \lambda_{2}L} \right)\frac{L}{2} = \left( \frac{\lambda_{2}}{\lambda_{1} + \lambda_{2}} \right).\frac{L}{2}$$x_{cm} + y_{cm} = \left( \frac{\lambda_{1} + \lambda_{2}}{\lambda_{1} + \lambda_{2}} \right).\frac{L}{2}$⇒ $x_{cm} + y_{cm} = \frac{L}{2}$

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