A thin metal wire of length L and uniform lin | vedclass

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

Question

(A) The total mass of the wire is $m = Q \cdot L$.Since the wire is bent into a circular coil of radius $R$,the circumference is $2 \pi R = L$,which g

Vedclass · Accepted Answer

$3 Q L^3 / 8 \pi^2$

Vedclass · Answer

(A) The total mass of the wire is $m = Q \cdot L$.Since the wire is bent into a circular coil of radius $R$,the circumference is $2 \pi R = L$,which gives $R = L / (2 \pi)$.The moment of inertia of a circular ring about its diameter is $I_{diam} = (1/2) m R^2$.Using the parallel axis theorem,the moment of inertia about the tangent axis $XX'$ is $I_{XX'} = I_{cm} + m R^2$,where $I_{cm}$ is the moment of inertia about the diameter passing through the center.$I_{XX'} = (1/2) m R^2 + m R^2 = (3/2) m R^2$.Substituting $m = Q L$ and $R = L / (2 \pi)$ into the expression:$I_{XX'} = (3/2) \cdot (Q L) \cdot (L / (2 \pi))^2$$I_{XX'} = (3/2) \cdot Q L \cdot (L^2 / (4 \pi^2))$$I_{XX'} = 3 Q L^3 / (8 \pi^2)$.

$A$ thin metal wire of length $L$ and uniform linear mass density $Q$ is bent into a circular coil with $O$ as the center. The moment of inertia of the coil about the axis $XX'$ is:

Similar Questions

$A$ rigid body of mass $m$ is rotating with angular velocity $\omega$ about an axis at a distance '$a$' from the center of mass $G$. The radius of gyration about an axis passing through $G$ is $K$. The rotational kinetic energy of this body about the new parallel axis will be:

$A$ solid sphere of mass $5 \ kg$ and radius $10 \ cm$ is kept in contact with another solid sphere of mass $10 \ kg$ and radius $20 \ cm$. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is . . . . . . $kg \cdot m^{2}$.

What is the moment of inertia of a ring of mass $M$ and radius $R$ about the axis $PQ$ as shown in the figure?

What is the moment of inertia of a disc about one of its diameters?

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing through the edge of the disc and normal to the disc is

Vedclass Test Series

Exam Paper Generator

Online Exam Module