Two particles having masses $m_{1}$ and $m_{2}$ are situated in a plane perpendicular to line AB at a distance of $r_{1}$ and $r_{2}$ respectively as shown. Find the moment of inertia about axis passing through centre of mass and perpendicular to line joining $m_{1}$ and $m_{2}$ .

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Solution

The correct option is A

Centre of mass of system $r_{c m}$ = $m_{2} \frac{r_{1} + r_{2}}{m_{1} + m_{2}}$ = distance of centre of mass from $m_{1}$

Distance of centre of mass from mass $m_{2}$ = $\frac{m_{1} (r_{1} + r_{2})}{(m_{1} + m_{2})}$

So moment of inertia about its centre of mass = $I_{C M}$ = $m_{1} (\frac{m_{2} (r_{1} + r_{2})}{m_{1} + m_{2}})^{2} + m_{2} (\frac{m_{1} (r_{1} + r_{2})}{m_{1} + m_{2}})^{2}$

$I_{c m}$ = $\frac{m_{1} m_{2} (r_{1} + r_{2})^{2}}{m_{1} + m_{2}}$

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Two particles having masses m1 and m2 are situated in a plane perpendicular to line AB at a distance of r1 and r2 respectively as shown. Find the moment of inertia about axis passing through centre of mass and perpendicular to line joining m1 and m2.

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