A uniform solid sphere of mass M , radius R and having moment of inertia about an axis passing through center of mass is I , is recast into a uniform circular disc of thickness t , whose moment of ine

Question

A uniform solid sphere of mass M , radius R and having moment of inertia about an axis passing through center of mass is I , is recast into a uniform circular disc of thickness t , whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I . Then radius of the disc will be

TestHub · Accepted Answer

I = 2 5 M R 2 and ρ = 3 M 4 π R 3 For circular disc π r 2 × t ρ = M ⇒ π r 2 ⋅ t ⋅ 3 M 4 π R 3 = M ⇒ t = 4 π R 3 3 π r 2 = 4 R 3 3 r 2 ⇒ r 2 = 4 R 3 3 t 2 5 M R 2 = 3 2 M R 2 ⇒ 2 5 R 2 = 3 2 ⋅ 4 R 3 3 t ⇒ t = 5 R ⇒ r 2 ⋅ 3 ⋅ 5 R = 4 R 3 ⇒ r 2 = 4 R 2 15 ⇒ r = 2 R 15

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