The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end, is

Question

The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end, is (A)  (ML2/3)  (B)  (ML2/12)  (C)  (ML2/2)  (D)  (ML2/13)

Tardigrade Admin · Accepted Answer

From theorem of parallel axis IA=IC+M( (L/2) )2 =(ML2/12)+(ML2/4) IA=(ML2/3)

Q. The moment of inertia of a straight thin rod of mass $M$ and length $L$ about an axis perpendicular to its length and passing through its one end, is

$\frac{M L ^{2}}{3}$

$\frac{M L ^{2}}{12}$

$\frac{M L ^{2}}{2}$

$\frac{M L ^{2}}{13}$

From theorem of parallel axis
$I_{A} = I_{C} + M (\frac{L}{2})^{2}$
$= \frac{M L ^{2}}{12} + \frac{M L ^{2}}{4}$
$I_{A} = \frac{M L ^{2}}{3}$

Q. The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end, is

3ML2​

12ML2​

2ML2​

13ML2​