Three thin rods,each of mass M and length L,a | vedclass

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

Question

(C) Let the three rods be $1$,$2$,and $3$ placed along the $X$,$Y$,and $Z$ axes respectively.$1$. The moment of inertia of rod $1$ (along $X$ axis) ab

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the three rods be $1$,$2$,and $3$ placed along the $X$,$Y$,and $Z$ axes respectively.$1$. The moment of inertia of rod $1$ (along $X$ axis) about the $Z$ axis: Since the rod lies along the $X$ axis,its distance from the $Z$ axis varies from $0$ to $L$. 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 $I = \frac{ML^2}{3}$. Thus,$I_1 = \frac{ML^2}{3}$.$2$. The moment of inertia of rod $2$ (along $Y$ axis) about the $Z$ axis: Similarly,the rod lies along the $Y$ axis,and the $Z$ axis is perpendicular to it at the origin. Thus,$I_2 = \frac{ML^2}{3}$.$3$. The moment of inertia of rod $3$ (along $Z$ axis) about the $Z$ axis: The rod lies along the $Z$ axis itself. Therefore,every mass element of the rod is at a distance of $0$ from the $Z$ axis. Thus,$I_3 = 0$.Total moment of inertia $I = I_1 + I_2 + I_3 = \frac{ML^2}{3} + \frac{ML^2}{3} + 0 = \frac{2 ML^2}{3}$.

Three thin rods,each of mass $M$ and length $L$,are placed along the $X$,$Y$,and $Z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $Z$ axis is:

Similar Questions

$Assertion$ : Moment of inertia depends on the axis of rotation and the nature of distribution of the mass of the body.
$Reason$ : Moment of inertia is the rotational inertia of the body.

Three particles,each of mass $m$,are placed at the vertices of an equilateral triangle $ABC$ of side length $l$. What is the moment of inertia of the system about the axis $AX$ in the plane of $ABC$,as shown in the figure?

Three balls of masses $2 \,kg$,$4 \,kg$,and $6 \,kg$ are placed at the midpoints of the sides of an equilateral triangle of side length $2 \,m$. The moment of inertia of the system about an axis passing through the centroid and perpendicular to the plane of the triangle is . . . . . .$kg \,m^2$.

The ratios of the masses and radii of two circular rings are $1:2$ and $2:1$ respectively. What is the ratio of their moments of inertia?

$A$ solid sphere of radius $10 \ cm$ is rotating about an axis which is at a distance $15 \ cm$ from its centre. The radius of gyration about this axis is $\sqrt{n} \ cm$. The value of $n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module