Question

Two point masses m and m and 3m are placed at distance r the moment of inertia of the system about an axis passing through the centre of mass of a system and perpendicular to the line joining to the point masses is

Answer 1

Answer:

3mr^2/4

Explanation:

Suppose the separation is r then the center of mass from the mass,m1 will be at a distance given by r1

= (m2/m1+m2)r

And the center of mass from the mass,m2 will be at a distance given by r2

= (m1/m1+m2)r

So the moment of inertia will be

i = i1 + i2

= m1r1^2 + m2r2^2

= {m1m2^2/(m1 + m2)^2}r^2 + {m2m1^2/(m1 + m2)^2}r^2

Putting m = m and m = 3m

we get i = 3mr^2/4