The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is

Question

The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is (A)  (ML2/12)  (B)  (ML2/9)  (C)  (7 ML2/48)  (D)  (ML2/48)

Tardigrade Admin · Accepted Answer

I CM =(M L2/12) (about middle point) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ddf6a2f37bfcc223ed0bef0e886d57f8-.png" /> ∴ I =I CM +M x2 =(M L2/12)+M((L/6))2 I =(M L2/9)

Q. The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $1/3$ from one of its ends and perpendicular to the rod is

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

$\frac{M L ^{2}}{9}$

$\frac{7 M L ^{2}}{48}$

$\frac{M L ^{2}}{48}$

$I_{CM} = \frac{M L ^{2}}{12}$ (about middle point)

$∴ I = I_{CM} + M x^{2}$
$= \frac{M L ^{2}}{12} + M (\frac{L}{6})^{2}$
$I = \frac{M L ^{2}}{9}$

Q. The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is

12ML2​

9ML2​

487ML2​

48ML2​