Question

the moment of inertia of a solid hemisphere of mass M and radius R about an axis passing through its centre of mass and parallel to its circular face is

Answer 1

Answer:

Since the center of mass of a solid hemisphere is 3/8 R above the circular base; so reducing it to a one particle system, and the moment of inertia of that one particle system isM(

8R

3

)

2

=M

64

9

×R

2

Now moment of inertia of the particle about an axis parallel to the original one but at a distance of 3/4 R can be obtained using the parallel axis theorem

new M.I = MR

2

64

45

so the radius of gyration =R(

64

45

)

2

1