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

$A$ thin circular disc is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z'$ axes will be

The theorem of perpendicular axes is applicable to which type of body?

$A$ circular thin disc of mass $2 \ kg$ has a diameter $0.2 \ m$. Calculate its moment of inertia about an axis passing through the edge and perpendicular to the plane of the disc (in $kg \cdot m^2$).

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Vedclass Test Series

Exam Paper Generator

Online Exam Module