The moment of inertia of a solid sphere of density ρ and radius R about its diameter is Options: A . &nbsp105176R5ρ B . &nbsp105176R2ρ C . &nbsp176105R5ρ D . &nbsp176105R2ρ

Answer: Option C : C Moment of inertia of sphere about it diameter I = 2 5 M R 2 = 2 5 ( 4 3 π R 3 ρ ) R 2 [ A s M = V ρ = 4 3 π R 3 ρ ] l = 8 π 15 R 5 ρ = 8 × 22 15 × 7 R 5 ρ = 176 105 R 5 ρ

The moment of inertia of a solid sphere of density ρ and radius R abo

Question

The moment of inertia of a solid sphere of density

ρ

and radius R about its diameter is

Options:

A . 105176R5ρ

B . 105176R2ρ

C . 176105R5ρ

D . 176105R2ρ

Answer: Option C
:
C
Moment of inertia of sphere about it diameter

I = \frac{2}{5} M R^{2} = \frac{2}{5} (\frac{4}{3} π R^{3} ρ) R^{2}

[A s M = V ρ = \frac{4}{3} π R^{3} ρ]

l = \frac{8 π}{15} R^{5} ρ = \frac{8 \times 22}{15 \times 7} R^{5} ρ = \frac{176}{105} R^{5} ρ

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