The moment of inertia of a uniform thin rod o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through its center of mass and perpendicular to the r

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through its center of mass and perpendicular to the rod is $I_{cm} = \frac{ML^2}{12}$.We need to find the moment of inertia about an axis at a distance $d = \frac{L}{3}$ from one end.The distance of this axis from the center of mass is $a = \frac{L}{2} - \frac{L}{3} = \frac{L}{6}$.Using the parallel axis theorem,$I = I_{cm} + Ma^2$.Substituting the values,$I = \frac{ML^2}{12} + M\left(\frac{L}{6}\right)^2$.$I = \frac{ML^2}{12} + \frac{ML^2}{36} = \frac{3ML^2 + ML^2}{36} = \frac{4ML^2}{36} = \frac{ML^2}{9}$.

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

Similar Questions

$A$ slender rod of mass $M$ and length $L$ is hinged at one end to swing freely in a vertical plane. Its density is non-uniform and varies linearly from the hinged end to the free end,doubling its value. The moment of inertia of the rod about the rotation axis passing through the hinge point is:

The radius of gyration of a rod of length $L$ and mass $M$ about an axis perpendicular to its length and passing through a point at a distance $L/3$ from one of its ends,is :-

Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is

Two circular discs of iron have the same thickness. The diameter of disc $A$ is twice that of disc $B$. The moment of inertia of $A$ will be ........ times that of $B$.

How does the moment of inertia depend on the angular momentum?

Vedclass Test Series

Exam Paper Generator

Online Exam Module