Identical rings are arranged in a hexagonal p | vedclass

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

Question

(A) The system consists of one central ring and six surrounding rings.$1$. For the central ring, the moment of inertia about the axis passing through

Vedclass · Accepted Answer

$31$

Vedclass · Answer

(A) The system consists of one central ring and six surrounding rings.$1$. For the central ring, the moment of inertia about the axis passing through its centre and normal to its plane is $I_{central} = MR^2$.$2$. For each of the six surrounding rings, the distance between the centre of the central ring and the centre of the surrounding ring is $d = 2R$.$3$. Using the parallel axis theorem, the moment of inertia of one surrounding ring about the axis passing through the centre of the central ring is $I_{surrounding} = I_{CM} + Md^2 = MR^2 + M(2R)^2 = MR^2 + 4MR^2 = 5MR^2$.$4$. Since there are six such surrounding rings, their total moment of inertia is $6 	imes 5MR^2 = 30MR^2$.$5$. The total moment of inertia of the system is $I_{total} = I_{central} + 30MR^2 = MR^2 + 30MR^2 = 31MR^2$.

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 moment of inertia of a solid sphere of mass $M$ and radius $R$ about its tangent is:

$A$ disc and a ring both have the same mass and radius. The ratio of the moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

From a disc of mass $M$ and radius $R$,a circular hole of diameter $R$ is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre is

Four rods,each of mass $M$ and length $l$,are arranged to form a square as shown in the figure. What is the moment of inertia of this square about an axis passing through $O$ and perpendicular to the plane of the square?

Vedclass Test Series

Exam Paper Generator

Online Exam Module