Four small objects, each of mass m, are fixed | vedclass

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

Question

(A) Let the rectangular frame have corners $A, B, C,$ and $D$ such that side $AD = BC = a$ and side $AB = CD = b$. The masses $m$ are placed at each c

Vedclass · Accepted Answer

$2 ma^{2}$

Vedclass · Answer

(A) Let the rectangular frame have corners $A, B, C,$ and $D$ such that side $AD = BC = a$ and side $AB = CD = b$. The masses $m$ are placed at each corner.The axis of rotation passes along the side of length $b$ (let this be side $CD$).The moment of inertia $I$ of a system of particles is given by $I = \sum m_i r_i^2$, where $r_i$ is the perpendicular distance of the $i$-th mass from the axis of rotation.$1$. The masses at $C$ and $D$ lie on the axis of rotation, so their perpendicular distances are $r_C = 0$ and $r_D = 0$. Thus, their contribution to the moment of inertia is $m(0)^2 + m(0)^2 = 0$.$2$. The masses at $A$ and $B$ are at a perpendicular distance $a$ from the axis $CD$. Thus, their contribution is $m(a)^2 + m(a)^2 = 2ma^2$.Therefore, the total moment of inertia of the system about the axis $CD$ is $I = 0 + 2ma^2 = 2ma^2$.

Four small objects, each of mass $m$, are fixed at the corners of a rectangular wire-frame of negligible mass with sides $a$ and $b$ $(a > b)$. If the wire frame is now rotated about an axis passing along the side of length $b$, then the moment of inertia of the system for this axis of rotation is:

Similar Questions

The figure shows a triangular lamina which can rotate about different axes. The moment of inertia is maximum about the axis:

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 body does not depend on

Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module