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

$A$ wire of mass $M$ is bent into a circular shape of radius $R$. What is the moment of inertia about its diameter?

The radius of gyration of a disc of mass $50 \, g$ and radius $2.5 \, cm$ about an axis passing through its center of gravity and perpendicular to its plane is ....... $cm$.

$A$ ring,a solid sphere,and a disc have the same mass and radius. Which of them has the largest moment of inertia?

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about its centre is:

The moment of inertia of a straight thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its one end,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module