The moment of inertia of a semicircular ring | vedclass

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

Question

(D) Let the center of the semicircular ring be $O$. The moment of inertia of a complete ring of mass $2M$ and radius $R$ about an axis passing through

Vedclass · Accepted Answer

$2MR^2$

Vedclass · Answer

(D) Let the center of the semicircular ring be $O$. The moment of inertia of a complete ring of mass $2M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is $I_{cm} = (2M)R^2$. By symmetry,the moment of inertia of the semicircular ring of mass $M$ about the axis passing through $O$ and perpendicular to the plane is $I_O = MR^2$. Now,we use the parallel axis theorem to find the moment of inertia about an axis passing through point $A$ and perpendicular to the plane. The distance between the center $O$ and point $A$ is $R$. The parallel axis theorem states $I_A = I_O + Md^2$,where $d = R$. Substituting the values,we get $I_A = MR^2 + M(R)^2 = 2MR^2$.

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

Similar Questions

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum?

The figure shows three identical discs,each of mass $M$ and radius $R$. Find the moment of inertia of this system about the axis $xx'$.

Let $I_1, I_2$ and $I_3$ be the moment of inertia of a uniform square plate of mass $M$ and side length $L$ about axes $AOC, xDx'$ and $yBy'$ respectively as shown in the figure. The ratio of the moments of inertia $I_1 : I_2 : I_3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module