Moment Of Inertia

The moment of inertia of a solid sphere about its diameter is given by:

I_%7B%5Ctext%7Bsolid%20sphere%7D%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D%20m%20r%5E2%2C

where

m

is the mass and

r

is the radius. For a solid sphere, the moment of inertia is

20%20%5C%2C%20%5Ctext%7Bkg%20m%7D%5E2

. Thus:

%5Cfrac%7B2%7D%7B5%7D%20m%20r%5E2%20%3D%2020.

From this, we can solve for

m%20r%5E2

m%20r%5E2%20%3D%20%5Cfrac%7B5%20%5Ctimes%2020%7D%7B2%7D%20%3D%2050.

For a thin spherical shell, the moment of inertia about its diameter is given by:

I_%7B%5Ctext%7Bshell%7D%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20m%20r%5E2.

Substitute

m%20r%5E2%20%3D%2050

I_%7B%5Ctext%7Bshell%7D%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%2050%20%3D%2033.3%20%5C%2C%20%5Ctext%7Bkg%20m%7D%5E2.

Thus, the correct answer is

33.3%20%5C%2C%20%5Ctext%7Bkg%20m%7D%5E2

Chapter Questions
1 MCQs