Question

Compare the moment of inertia of a disk of mass 2m and radius R about its central axis to the moment of inertia of a sphere of mass m and radius 2R.

Answer 1

`(I_(disc))/(I_(sphere)) = (5)/(8)`

Step-by-step explanation:

As we know that the moment of inertia of the disc is given as

`I_(disc) = (1)/(2)mR^2`

here we know that

`mass = 2m`

`radius = R`

`I_(disc) = mR^2`

Now for sphere the moment of inertia is given as

`I_(sphere) = (2)/(5)mR^2`

here we know that

`mass = m`

`radius = 2R`

`I_(disc) = (2)/(5)m(2R)^2= (8)/(5)mR^2`

now the ratio of two moment of inertia is

`(I_(disc))/(I_(sphere)) = (mR^2)/(1.6mR^2)`

`(I_(disc))/(I_(sphere)) = (5)/(8)`