I_1 is the moment of inertia of a circular di | vedclass

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

Question

(D) Using the parallel axis theorem,$I_2 = I_{CM} + Mh^2$.For a circular disc,the moment of inertia about an axis passing through its centre and perpe

Vedclass · Accepted Answer

$17$

Vedclass · Answer

(D) Using the parallel axis theorem,$I_2 = I_{CM} + Mh^2$.For a circular disc,the moment of inertia about an axis passing through its centre and perpendicular to its plane is $I_1 = I_{CM} = \frac{1}{2}MR^2$.The distance between the parallel axes is $h = \frac{2R}{3}$.Substituting these values into the parallel axis theorem:$I_2 = \frac{1}{2}MR^2 + M\left(\frac{2R}{3}ight)^2$$I_2 = \frac{1}{2}MR^2 + M\left(\frac{4R^2}{9}ight)$$I_2 = MR^2 \left(\frac{1}{2} + \frac{4}{9}ight) = MR^2 \left(\frac{9 + 8}{18}ight) = \frac{17}{18}MR^2$.Now,find the ratio $\frac{I_2}{I_1}$:$\frac{I_2}{I_1} = \frac{\frac{17}{18}MR^2}{\frac{1}{2}MR^2} = \frac{17}{18} 	imes 2 = \frac{17}{9}$.Comparing this with the given ratio $\frac{x}{9}$,we get $x = 17$.

Similar Questions

Three rods are arranged in the form of an equilateral triangle. Calculate the moment of inertia about an axis passing through the centroid and perpendicular to the plane of the triangle. (Each rod has mass $M$ and length $L$)

$A$ uniform disc of radius $R$ lies in the $x-y$ plane with its centre at the origin. Its moment of inertia about the $z$-axis is equal to its moment of inertia about the line $y = x + c$. The value of $c$ is

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

What is the moment of inertia of a thin rod of length $L$ and mass $M$ about an axis perpendicular to the rod and passing through a point at a distance of $L/3$ from one of its ends?

Vedclass Test Series

Exam Paper Generator

Online Exam Module