Three thin uniform rods,each of mass M and le | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{2ML^2}{3}$

Vedclass · Answer

(B) The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through one of its ends and perpendicular to its length is $I = \frac{ML^2}{3}$.For the given system:$1$. The rod along the $x$-axis lies in the $xz$-plane. Its moment of inertia about the $z$-axis is $I_x = \frac{ML^2}{3}$.$2$. The rod along the $y$-axis lies in the $yz$-plane. Its moment of inertia about the $z$-axis is $I_y = \frac{ML^2}{3}$.$3$. The rod along the $z$-axis lies along the axis of rotation itself. Since the rod is thin,the distance of every mass element from the $z$-axis is zero. Therefore,its moment of inertia about the $z$-axis is $I_z = 0$.The total moment of inertia of the system about the $z$-axis is $I_{total} = I_x + I_y + I_z = \frac{ML^2}{3} + \frac{ML^2}{3} + 0 = \frac{2ML^2}{3}$.

Three thin uniform rods,each of mass $M$ and length $L$,are placed along the three Cartesian axes such that one end of each rod is at the origin. Find the moment of inertia of this system about the $z$-axis.

Similar Questions

Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis along any one side of the triangle is:

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

Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is $M$,radius of its top is $R$,and height is $H$,then its moment of inertia about its axis is

The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its center on the $x$-axis at a distance $a$ from the origin. Then,the moment of inertia of the disc about the $x$-axis is:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module