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 sa

Question

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.

TestHub · Accepted Answer

I 1 ​ = 4 MR 1 2 ​ ​ , I 2 ​ = 2 MR 2 2 ​ ​ , I 3 ​ = 5 2 MR 1 2 ​ ​ According to problem I 2 ​ I 1 ​ ​ = 2.5 ⇒ 2 MR 2 2 ​ ​ 4 MR 1 2 ​ ​ ​ = 2 5 ​ ⇒ R 2 2 ​ R 1 2 ​ ​ = 5 … Now we are provided with information that ​ I 2 ​ I 3 ​ ​ = n ⇒ 2 MR 2 2 ​ ​ 5 2 MR 1 2 ​ ​ ​ = n ⇒ 5 R 2 2 ​ 4 R 1 2 ​ ​ = n ​ From Eq', (1) and (2) ⇒ n = 4

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