Question

find MOI of rod mass M1 length L about perpendicular to axis

Answer 1

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please refer to the attachment above ..
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Answer 2

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) (using formula)

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

now moment of inertia of two particles is

I1 = m1r12 & I2 = m2r22

I = I1+I2 = m1r12 + m2r22

from 2 & 3 above expression becomes

I = m1m2r2/(m1+m2)

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