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Two point masses m₁ and m₂ and attached from two ends of a rod of negligible mass. The system is rotated about an axis perpendicular to the length of the rod. The minimum moment of inertia of the system is

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about centre of mass

$\frac{m_{1} m_{2} l^{2}}{m_{1} + m_{2}}$

Both about centre of mass and $\frac{m_{1} m_{2} l^{2}}{m_{1} + m_{2}}$

None of the above

answer is C.

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Detailed Solution

Minimum moment of inertia is about centre of mass.

$I_{\min} = m_{1} r_{_{1}}^{2} + m_{2} r_{_{2}}^{2} = m_{1} {(\frac{m_{2}}{m_{1} + m_{2}} l)}^{2} + m_{2} {(\frac{m_{1}}{m_{1} + m_{2}} l)}^{2} = (\frac{m_{1} m_{2}}{m_{1} + m_{2}}) l^{2}$

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