# 24) The moment of inertia of a disc about an axis tangential and parallel to it's surface be I, then what will be the moment of Inertia about the axis tangential but perpendicular to the surface.25) A solid sphere ball rolls on an inclined plane without slipping. The ratio of the rotational energy and rolling energy.

Refer to the following figure

here

moment of inertia about tangential axis will be

[using parallel axis theorem]

IT = IX + MR2

= (1/4)MR2 + MR2

so,

IT = I =  (5/4)MR2

(4/5)I = MR2.....................(1)

now,

moment of inertia about the axis of symmetry i.e. z-axis [refer to NCERT table for this]

IZ = (1/2)MR2 .....................(2)

thus, moment of inertia about an axis that is tangential and parallel to the surface of the disc will be

Ia = IZ + MR2

= (1/2)MR2 + MR2

so,

Ia = (3/2)MR2

now, form (1)

Ia = (3/2) x [(4/5)I]

thus, we get

Ia = (6/5)I

..

2.

If a spherical ball rolls on a table without slipping then it will only possesses Rotational energy while total energy will be the sum of rotational and translational energy:

rotational energy / total energy = RE / (KE + RE) =

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