Solve the problem.
-Find the moment of inertia of a sphere of radius 9 and constant density $\delta$ about a diameter.
A) $39,366 \delta \pi$
B) $\frac { 157,464 } { 5 } \delta \pi$
C) $\frac { 137,781 } { 4 } \delta \pi$
D) $\frac { 177,147 } { 5 } \delta \pi$

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere of radius $r$ and constant density $\delta$ about a diameter is given by the formula $\frac{2}{5}mr^2$, where $m$ is the mass of the sphere. The mass $m$ can be expressed as $\delta V$, where $V$ is the volume of the sphere, $V = \frac{4}{3}\pi r^3$. Substituting $r = 9$ and simplifying gives the moment of inertia as $\frac{2}{5} \delta \frac{4}{3} \pi 9^3 = \frac{2}{5} \delta \frac{4}{3} \pi 729 = \frac{8}{15} \delta \pi 729 = \frac{157,464}{5} \delta \pi$.

Solve the Problem δ\deltaδ About a Diameter 39,366δπ39,366 \delta \pi39,366δπ B) 157,4645δπ\frac { 157,464 } { 5 } \delta \pi5157,464​δπ

Solve the Problem $\delta$ About a Diameter $39,366 \delta \pi$ B) $\frac { 157,464 } { 5 } \delta \pi$