# Four holes of radius R are cut from a thin square plate of the side 4R and mass M in XY plane as shown. Then moment of inertia of the remaining portion about z-axis is=? Plz explain clearly!!

##### 1 Answer

Apr 12, 2018

#### Explanation:

For the

# I_(zz)=1/12 m (h^2+w^2) #

That's for rotation around an axis perpendicular to it's centre.

The plate has density

A single disc, therefore, has mass:

A disc's inertia about it's centre is therefore:

Using the parallel axis theorem (see drawing):

So the inertia of the hollowed out plate is: