
consider this hollow cone ,now cut a ring of thickness dx at a distance x from the origin ,
so radius of the ring will be r'=xtanΘ where Θ is the half angel of cone
so moment of inertia of this ring is dI =dm r'2
dm =[ M/πrL ]2πr'dL where L is slant hight
=[2M/rL]r'dx/cosΘ
so dI =[2M/rL]r'3dx/cosΘ
=tan3Θ/cosΘ [2M/rL]x3dx
=tan3Θ [2M/rh]x3dx
I =o∫h tan3Θ [2M/rh]x3dx
I=mr2/2 !!!!!
hii
consider this hollow cone ,now cut a ring of thickness dx at a distance x from the origin ,
so radius of the ring will be r'=xtanΘ where Θ is the half angel of cone
so moment of inertia of this ring is dI =dm r'2
dm =[ M/πrL ]2πr'dL where L is slant hight
=[2M/rL]r'dx/cosΘ
so dI =[2M/rL]r'3dx/cosΘ
=tan3Θ/cosΘ [2M/rL]x3dx
=tan3Θ [2M/rh]x3dx
I =o∫h tan3Θ [2M/rh]x3dx
I=mr2/2 !!!!!