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Q.

A light rod of length l has two masses m1and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

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a

m1m2m1+m2l2

b

m1+m2m1+m2l2

c

m1+m2l2

d

m1m2l2

answer is A.

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Detailed Solution

Here, l1+l2=lCentre of mass of the system,l1=m1×0+m2×lm1+m2=m2lm1+m2l2=l-l1=m1lm1+m2Required moment of inertia of the systemI=m1l12+m2l22=m1m22+m2m12l2m1+m22=m1m2m1+m2l2m1+m22=m1m2m1+m2l2
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A light rod of length l has two masses m1and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is