A uniform circular disc of radius R and mass | vedclass

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

Question

(D) The moment of inertia of the original disc of mass $M$ and radius $R$ about the central axis is $I_1 = \frac{1}{2} MR^2$.The mass of the removed c

Vedclass · Accepted Answer

$\frac{13}{32} MR^2$

Vedclass · Answer

(D) The moment of inertia of the original disc of mass $M$ and radius $R$ about the central axis is $I_1 = \frac{1}{2} MR^2$.The mass of the removed circular part of radius $r = R/2$ is $M' = \frac{M}{\pi R^2} 	imes \pi (R/2)^2 = M/4$.The moment of inertia of this removed part about its own central axis is $I_{cm} = \frac{1}{2} M' r^2 = \frac{1}{2} (M/4) (R/2)^2 = \frac{1}{32} MR^2$.Using the parallel axis theorem,the moment of inertia of the removed part about the original central axis of the disc (at a distance $d = R/2$ from its own center) is $I_2 = I_{cm} + M' d^2 = \frac{1}{32} MR^2 + (M/4) (R/2)^2 = \frac{1}{32} MR^2 + \frac{1}{16} MR^2 = \frac{3}{32} MR^2$.The moment of inertia of the remaining part is $I = I_1 - I_2 = \frac{1}{2} MR^2 - \frac{3}{32} MR^2 = \frac{16-3}{32} MR^2 = \frac{13}{32} MR^2$.

Similar Questions

What is the moment of inertia of a ring of mass $M$ and radius $R$ about a tangent to the circle of the ring in its own plane?

If $I$ is the moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of the disc,what is the moment of inertia of the same circular disc about an axis perpendicular to the plane and passing through its centre?

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

The rectangular block shown in the figure is rotated about the $x-x$,$y-y$,and $z-z$ axes passing through its center of mass $O$. Its moment of inertia is:

Each spherical shell has a radius $R$ and mass $M$. They are connected by a light massless rod. Calculate the moment of inertia about the axis $xx'$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module