A quarter of a uniform circular disc of radiu | vedclass

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

Question

(A) The moment of inertia of a complete uniform circular disc of mass $M_{total}$ and radius $R$ about an axis passing through its center and perpendi

Vedclass · Accepted Answer

$\frac{1}{2} M R^2$

Vedclass · Answer

(A) The moment of inertia of a complete uniform circular disc of mass $M_{total}$ and radius $R$ about an axis passing through its center and perpendicular to its plane is $I = \frac{1}{2} M_{total} R^2$.Since the disc is uniform,the mass is proportional to the area. $A$ quarter of the disc has an area equal to one-fourth of the total area.Therefore,the mass of the full disc would be $M_{total} = 4M$.The moment of inertia of the full disc about the given axis is $I_{full} = \frac{1}{2} (4M) R^2 = 2 M R^2$.Since the moment of inertia is an additive property for parts of a rigid body,the moment of inertia of the quarter disc $(I_{quarter})$ is one-fourth of the moment of inertia of the full disc about the same axis.$I_{quarter} = \frac{1}{4} I_{full} = \frac{1}{4} (2 M R^2) = \frac{1}{2} M R^2$.

$A$ quarter of a uniform circular disc of radius $R$ is cut off. The mass of the cut-off part is $M$. It rotates about an axis passing through the center of the original disc and perpendicular to the plane of the disc. What will be its moment of inertia about the axis of rotation?

Similar Questions

Of the two eggs which have identical sizes,shapes and weights,one is raw and the other is half-boiled. The ratio between the moment of inertia of the raw egg to the half-boiled egg about their central axis is

We have a rectangular plate of uniform thickness. $E, F, G, H$ are the midpoints of $AB, BC, CD,$ and $AD$ respectively. About which axis will the moment of inertia be minimum?

$A$ thin wire of length $L$ and uniform linear mass density $\lambda$ is bent into a circular ring. The moment of inertia of the ring about a tangential axis in its plane is:

Three thin rods,each of mass $M$ and length $L$,are placed along the $X$,$Y$,and $Z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $Z$ axis is:

Two rods each of mass $m$ and length $\ell$ are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through the common center and perpendicular to the plane formed by them?

Vedclass Test Series

Exam Paper Generator

Online Exam Module