Question

The moment of inertia of a uniform thin rod of lenght L and mass M about an axis passing through a point at a distance of L/3 from one of its ends and perpendicular to the rod is:

• A. $\frac { 7 \mathrm { ML } ^ { 2 } } { 48 }$
• B. $\frac { \mathrm { ML } ^ { 2 } } { 9 }$
• C. $\frac { \mathrm { ML } ^ { 2 } } { 12 }$
• D. $\frac { \mathrm { ML } ^ { 2 } } { 3 }$

Answer 1

Answer: (B)

$\frac { \mathrm { ML } ^ { 2 } } { 9 }$

Answer 2

$I _ { c m } = \frac { M L ^ { 2 } } { 12 }$ (about middle point)

∴$I = I _ { c m } + M x ^ { 2 }$ $= \frac { M L ^ { 2 } } { 12 } + M \left( \frac { L } { 6 } \right) ^ { 2 } = \frac { M L ^ { 2 } } { 9 }$