Question

The moment of inertia of a solid sphere of density $\rho$ and radius R about its diameter is

• A. $\frac { 105 } { 176 } R ^ { 5 } \rho$
• B. $\frac { 105 } { 176 } R ^ { 2 } \rho$
• C. $\frac { 176 } { 105 } R ^ { 5 } \rho$
• D. $\frac { 176 } { 105 } R ^ { 2 } \rho$

Answer 1

Answer: (C)

$\frac { 176 } { 105 } R ^ { 5 } \rho$

Answer 2

Moment of inertia of sphere about it diameter

$I = \frac { 2 } { 5 } M R ^ { 2 }$ $= \frac { 2 } { 5 } \left( \frac { 4 } { 3 } \pi R ^ { 3 } \rho \right) R ^ { 2 }$ [As $M = V \rho$= $\frac { 4 } { 3 } \pi R ^ { 3 } \rho$ ]

I =$\frac { 8 \pi } { 15 } R ^ { 5 } \rho$ $= \frac { 8 \times 22 } { 15 \times 7 } R ^ { 5 } \rho = \frac { 176 } { 105 } R ^ { 5 } \rho$