Four thin metal rods,each of mass M and lengt | vedclass

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

Question

(D) To find the moment of inertia of the square frame about an axis passing through its center $O$ and perpendicular to its plane,we use the parallel

Vedclass · Accepted Answer

$\frac{4 ML^2}{3}$

Vedclass · Answer

(D) To find the moment of inertia of the square frame about an axis passing through its center $O$ and perpendicular to its plane,we use the parallel axis theorem for each rod.For a single rod of mass $M$ and length $L$,the moment of inertia about an axis passing through its center of mass and perpendicular to its length is $I_{cm} = \frac{ML^2}{12}$.The distance from the center of the square to the center of each rod is $d = \frac{L}{2}$.Using the parallel axis theorem,the moment of inertia of one rod about the axis passing through the center of the square is $I_{rod} = I_{cm} + Md^2 = \frac{ML^2}{12} + M(\frac{L}{2})^2 = \frac{ML^2}{12} + \frac{ML^2}{4} = \frac{ML^2 + 3ML^2}{12} = \frac{4ML^2}{12} = \frac{ML^2}{3}$.Since there are four such rods,the total moment of inertia of the system is $I_{total} = 4 	imes I_{rod} = 4 	imes \frac{ML^2}{3} = \frac{4ML^2}{3}$.

Four thin metal rods,each of mass $M$ and length $L$,are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

Similar Questions

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length $4R$. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

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

The moment of inertia of a solid sphere about its diameter is $I$. Two such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $AB$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module