For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = R ]

Question

For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = R ] (A) R2 (B) R3 (C) R4 (D) R5

Tardigrade Admin · Accepted Answer

Moment of inertia of a solid sphere is (2/5)mR2 I=(2/5)mR2 I=(2/5)Vρ R2 I=(2/5)× (4/3)π R3ρ R2 I=(8/15)π ρ R5 I propto R5

Q. For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = $R$ ]

$R^{2}$

$R^{3}$

$R^{4}$

$R^{5}$

Moment of inertia of a solid sphere is $\frac{2}{5} m R^{2}$
$I = \frac{2}{5} m R^{2}$
$I = \frac{2}{5} V ρ R^{2}$
$I = \frac{2}{5} \times \frac{4}{3} π R^{3} ρ R^{2}$
$I = \frac{8}{15} π ρ R^{5}$
$I \propto R^{5}$

Q. For a sphere made out of a certain material, the moment of inertia of the sphere is proportional to [radius of the sphere = R ]

R2

R3

R4

R5