The square structure shown in Fig. consists of lour point masses connected by rods of negligible Find the moment of inertia of the structure about the following axes: (a) axis `A`, passing through the centre of the structure and normal to its plane, (b) axis `B` passing through one of the point masses and normal to the plane of the structure, (c) axis `"CC"'`, passing through two adjacent point masses and (d) axis `"DD"'`, along the diagonal of the structure.

Explanation

a. `I_(A)=4[m(a/(sqrt(2)))^(2)]=2ma^(2)`
b. `I_(B)=2[ma^(2)]+m(sqrt(2))^(2)=4ma^(2)`
c. `I_(C)+2[ma^(2)]=2ma^(2)`
d. `I_(D)=2[m(a/(sqrt(2)))^(2)=]ma^(2)`