The moment of inertia of a uniform thin rod of length 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

Question

The moment of inertia of a uniform thin rod of length 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) (7 M L2/48) (B) (M L2/9) (C)  (ML2/12)  (D)  (ML2/3)

Tardigrade Admin · Accepted Answer

The moment of inertia about middle point

I_{CM} = \frac{M L ^{2}}{12}

From theorem of parallel axis theorem

∴ I = I_{CM} + M x^{2}

= \frac{M L ^{2}}{12} + M (\frac{L}{6})^{2}

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

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

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

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

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

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

The moment of inertia about middle point

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

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

487ML2​

9ML2​

12ML2​

3ML2​