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Two particles of masses m1 and m2 are connected by a light rod of length r to constitute a dumb-bell.The moment of inertia of the dumb=bell about an axis perpendicular to the rod passing through the center of mass of the two particles is

Two particles of masses m1 and m2 are connected by a light rod of length r to constitute a dumb-bell.The moment of inertia of the dumb=bell about an axis perpendicular to the rod passing through the center of mass of the two particles is 

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

consider a rod , two particles of mass m1 , m2 are at its two ends then

distance of center of mass from m1 is r1= m2r/(m1+m2)       ..........1                    (using formula)

distance of center of mass from m2 is r2 = m1r/(m1+m2)          .........2

now moment of inertia of two particles is

I1 = m1r12 & I2 = m2r22

I = I1+I2 = m1r12 + m2r22            ................3

from 2 & 3 above expression becomes

I = m1m2r2/(m1+m2)

approve my ans if u like ....

also see  question new13 , i have posted the ans

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