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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 r1and r2 respectively as shown.

Find the moment of intertia about axis passing through centre of mass and perpendicular to line joining m1 and m2


A

m1m2m1+m2 (r1+r2)2

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B

m1m2m1+m2 (r1r2)2

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C

m1m2m1+m2 (r21+r22)

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D

m1m2m1+m2 (r21+r22)

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Solution

The correct option is A

m1m2m1+m2 (r1+r2)2


Centre of mass of system rcm=m2(r1+r2)(m1+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 I=m1[m2(r1+r2)(m1+m2)]2+m1[m2(r1+r2)(m1+m2)]2=m1m2(r1+r2)2(m1+m2)


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