Question

The moment of inertia of a thin rod of mass M and length L about an axis perpendicular to te rod at a distance L/4 from one end is:

• A. $\frac { \mathrm { ML } ^ { 2 } } { 6 }$
• B. $\frac { \mathrm { ML } ^ { 2 } } { 12 }$
• C. $\frac { 7 \mathrm { ML } ^ { 2 } } { 24 }$
• D. $\frac { 7 \mathrm { ML } ^ { 2 } } { 48 }$

Answer 1

Answer: (D)

$\frac { 7 \mathrm { ML } ^ { 2 } } { 48 }$

Answer 2

$I = I _ { \mathrm { cm } } + M x ^ { 2 } = \frac { M L ^ { 2 } } { 12 } + M \left( \frac { L } { 4 } \right) ^ { 2 }$ $= \frac { M L ^ { 2 } } { 12 } + \frac { M L ^ { 2 } } { 16 } = \frac { 7 M L ^ { 2 } } { 48 }$