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Question

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.


A

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B

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C

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D

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Solution

The correct option is A


Centre of mass of system rcm = m2r1+r2m1+m2 = distance of centre of mass from m1

Distance of centre of mass from mass m2 = m1(r1+r2)(m1+m2)

So moment of inertia about its centre of mass = ICM = m1(m2(r1+r2)m1+m2)2+m2(m1(r1+r2)m1+m2)2

Icm = m1m2(r1+r2)2m1+m2


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