System of Particles and Rotational Motion · Question 50

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, n = . Consider all the bodies have equal masses.

Answer

4

Solution

Let radius of disc = sphere = R, radius of ring = r, common mass M.

About a diameter: Idisc = MR24, Iring = Mr22

Idisc = 2.5 Iring MR24 = 2.5 Mr22 R2 = 5r2

Isphere = 25MR2 = 25M(5r2) = 2Mr2

n = IsphereIring = 2Mr2Mr2/2 = 4

Answer: 4