Question

What is the moment of inertia of a solid sphere of density ρ and radius R about its diameter? 

(A) (105 / 176) R⁵ρ 

(B) (176 / 105) R⁵ρ 

(C) (105 / 176) R²ρ 

(D) (176 / 105) R²ρ

Answer 1

Correct option: (B) (176 / 105) R⁵ρ

Explanation:

For sphere MI = (2/5)MR² 

Density = [(mass) / (volume)] hence ρ = (M / ѵ)

M = ρѵ

= ρ ∙ (4/3)πR³ 

hence MI = (2/5) × (4/3)πR³ × R² × ρ = (8 / 15)πR⁵ρ 

= R⁵ ∙ ρ × [(176) / (105)] = [(176) / (105)]R⁵ρ