Four spheres of diameter 2a and mass M each are placed with their centres at four corners of a square - Physics - System Of Particles And Rotational Motion

Question

Four spheres of diameter 2a and mass M each are placed with
their centres at four corners of a square of side b Calculate the
moment of inertia of the system about one side of the square taken
as its axis ?

Kulshekhar Mehta · Accepted Answer

<img alt="" src=
"https://img-nm%20mnimgs%20com/img/study_content/content_ck_images/images/moment%20png"
style="width: 456px; height: 340px;">
Here Icm for any sphere is Icm=25Ma2
If one side of square is taken as axis then moment of inertia about
this axis is given by
I=Icm+ Mb2I =25Ma2+Mb2 (1) for a sphere about axis of rotation
Hence required moment of inertia is
Inet=2(25Ma2)+2(25Ma2+Mb2)=85Ma2+2Mb2=85M(a2+10b2)

Four spheres of diameter 2a and mass M each are placed with their centres at four corners of a square of side b. Calculate the moment of inertia of the system about one side of the square taken as its axis ?