The moment of inertia of a solid sphere about its diameter is 64 kg m². If that sphere is recast into eight identical smaller spheres, then the moment of inertia of one such small sphere about its diameter is ______ kg m².
Physics · Mixed Chapter
JEE Main Practice

Question

The moment of inertia of a solid sphere about its diameter is 64 kg m². If that sphere is recast into eight identical smaller spheres, then the moment of inertia of one such small sphere about its diameter is ______ kg m².

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a uniform solid sphere, I = (2/5)MR². Step 2: Recasting the same mass into eight identical spheres gives mass m = M/8 for each. Step 3: Volume ∝ R³. Each new sphere has volume 1/8 of original, so its radius r = R/2. Step 4: Iₛₘₐₗₗ/Iₒᵣᵢg = (m/M)(r/R)² = (1/8)(1/2)² = 1/32. Step 5: Iₛₘₐₗₗ = 64/32 = 2 kg m². Final answer: 2.