Question

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.

Answer 1

Explanation:

Moment of inertia about an axis

I axis = 6I/5

Answer 2

25)

for a solid sphere, I =2/5MR^2......(1)

and v=Rw ( for no slipping )

Rotational kinetic energy,

Er= Iw^2

=1/2 (2/5 MR^2)w^2 ....... ( from 1)

= 1/5 Mv^2

Total kinetic energy,

K.E.= 1/2MR^2+1/2Iw^2

= 1/2MR^2 + 1/2(2/5MR^2)w^2.... (from 1)

= 7/10 Mv^2

Hence, the ratio,

Er/E = 2/7