A small circular disc of radius R/3 is cut fr | vedclass

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

Question

(A) The moment of inertia of the full disc about point $O$ is:$I_{full} = \frac{1}{2}(9M)R^2 = \frac{9}{2}MR^2$ . . . $(i)$The radius of the removed d

Vedclass · Accepted Answer

$4MR^2$

Vedclass · Answer

(A) The moment of inertia of the full disc about point $O$ is:$I_{full} = \frac{1}{2}(9M)R^2 = \frac{9}{2}MR^2$ . . . $(i)$The radius of the removed disc is $r = R/3$. Since the mass is proportional to the area $(M \propto R^2)$,the mass of the removed disc is $m = 9M 	imes (r/R)^2 = 9M 	imes (1/3)^2 = M$.The moment of inertia of the removed disc about its own center of mass is:$I_{cm} = \frac{1}{2}m r^2 = \frac{1}{2}M(R/3)^2 = \frac{1}{18}MR^2$.Using the parallel axis theorem,the moment of inertia of the removed disc about point $O$ is:$I_{removed} = I_{cm} + m d^2$,where $d = 2R/3$ is the distance from $O$ to the center of the removed disc.$I_{removed} = \frac{1}{18}MR^2 + M(2R/3)^2 = \frac{1}{18}MR^2 + \frac{4}{9}MR^2 = \frac{1+8}{18}MR^2 = \frac{9}{18}MR^2 = \frac{1}{2}MR^2$.The moment of inertia of the remaining disc is:$I_{remaining} = I_{full} - I_{removed} = \frac{9}{2}MR^2 - \frac{1}{2}MR^2 = \frac{8}{2}MR^2 = 4MR^2$.

$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

Similar Questions

Moment of inertia of a disc about a diameter is $I$. Find the moment of inertia of the disc about an axis perpendicular to its plane and passing through its rim. (in $I$)

$A$ thin wire of length $L$ has a uniform linear mass density $\rho$. It is bent into a circular loop with center $O$. Calculate the moment of inertia of the circular loop about the axis $XX'$ as shown in the figure.

State the theorem of perpendicular axes and the theorem of parallel axes.

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