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 system consists of three rods placed along the $x$,$y$,and $z$ axes.Let $I_x$,$I_y$,and $I_z$ be the moments of inertia of the individual rods

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The system consists of three rods placed along the $x$,$y$,and $z$ axes.Let $I_x$,$I_y$,and $I_z$ be the moments of inertia of the individual rods about the $z$-axis.$1$. For the rod along the $z$-axis: The rod lies on the axis of rotation,so its moment of inertia about the $z$-axis is $I_1 = 0$.$2$. For the rod along the $x$-axis: The rod is perpendicular to the $z$-axis at one end. The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through one end and perpendicular to the rod is $I_2 = \frac{ML^2}{3}$.$3$. For the rod along the $y$-axis: Similarly,the rod is perpendicular to the $z$-axis at one end. The moment of inertia is $I_3 = \frac{ML^2}{3}$.The total moment of inertia of the system about the $z$-axis is $I = I_1 + I_2 + I_3 = 0 + \frac{ML^2}{3} + \frac{ML^2}{3} = \frac{2ML^2}{3}$.

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

Similar Questions

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_c$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_d : K_c$ is

$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. If their moments of inertia about their diameters are $I_A$ and $I_B$ respectively,then which of the following is true?

Three identical rods each of mass $M$ and length $L$ are joined to form a symbol $H$. The moment of inertia of the system about one of the sides of $H$ is

Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is in the plane of the cross and bisects the angle between the rods).

Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

Vedclass Test Series

Exam Paper Generator

Online Exam Module