Find moment of inertia of the of the following object Radius

Find moment of inertia of the of the following object. Radius of cylinder = R radius of spherical cavities = R/2 height of cylinder = 2R Mass of solid cylinder without any cavities = M I_cyclinder 1/2MR^2 Moment of inertia of solider sphere of mass m and radius r -2/5mr^2

Solution

Total moment of inertia = Icylinder + Icavity1 + Icavity2 .........(equ. 1)

Given

Icyclinder = `1/2 MR²

moment of inertia of soild sphere = 2/5 mr²

given r = R/2 and m = M

so Icavity1 = icavity2 = 2/5 M (R/2)²

                              = 2/5 M (R²/4)

                              = MR² / 10

from equ 1

total moment of inertia = 1/2 MR² + MR² /10 + MR² /10

                                 =7/10 MR²