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Show that the moment of inertia of a spherical shell of radius R and mass M...

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Physics

Show that the moment of inertia of a spherical shell of radius Rand mass M about an axis through
its centre is 2/3 MR2. Show also that the moment of inertia of auniform solid sphere of radius R and

mass M is 2/5MR2. The spheres are allowed to roll (from rest),without slipping a distance L down
a plane inclined at a angle θ to the horizontal. Find expressionsfor the speeds of the spheres at the
bottom of the incline and show that ∆v/〈v〉 = 8.7% where ∆v is thedifference in the speeds and 〈v〉 is

the mean of the two speeds. Which sphere has the largerspeed?

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