A solid sphere and hollow shell of same mass have same moment of inertia about their diameters. What is the ratio of their diameters?

Solution

Let R_s and R_b be the radii of solid sphere and hollow sphere respectively. Since solid sphere and hollow sphere have same moment of inertia,

therefore space space space 2 over 3 MR subscript straight h squared equals 2 over 5 MR subscript straight s squared space rightwards double arrow space space space straight R subscript straight s squared over Rh squared equals 5 over 3 space rightwards double arrow space space space space straight R subscript straight s over straight R subscript straight h equals square root of 5 over 3 end root

This is the required ratio of their diameters.

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