The ratio of radii of gyration of a ring to a | vedclass

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

Question

(A) The moment of inertia of a body is given by $I = Mk^2$,where $k$ is the radius of gyration.For a ring of mass $M$ and radius $R$ about a tangentia

Vedclass · Accepted Answer

$\frac{2}{\sqrt{3}}$

Vedclass · Answer

(A) The moment of inertia of a body is given by $I = Mk^2$,where $k$ is the radius of gyration.For a ring of mass $M$ and radius $R$ about a tangential axis perpendicular to its plane,using the parallel axis theorem: $I_{	ext{ring}} = I_{	ext{cm}} + MR^2 = MR^2 + MR^2 = 2MR^2$.Thus,$Mk_{	ext{ring}}^2 = 2MR^2 \implies k_{	ext{ring}} = \sqrt{2}R$.For a disc of mass $M$ and radius $R$ about a tangential axis perpendicular to its plane,using the parallel axis theorem: $I_{	ext{disc}} = I_{	ext{cm}} + MR^2 = \frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2$.Thus,$Mk_{	ext{disc}}^2 = \frac{3}{2}MR^2 \implies k_{	ext{disc}} = \sqrt{\frac{3}{2}}R$.The ratio of the radii of gyration is $\frac{k_{	ext{ring}}}{k_{	ext{disc}}} = \frac{\sqrt{2}R}{\sqrt{3/2}R} = \frac{\sqrt{2}}{\sqrt{3}/\sqrt{2}} = \frac{2}{\sqrt{3}}$.

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass,about a tangential axis perpendicular to the plane is

Similar Questions

$A$ one-quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

The radius of gyration of a body depends upon:

$A$ wire of mass $M$ is bent into a circular shape of radius $R$. What is the moment of inertia about its diameter?

$A$ solid square plate is spun around different axes with the same angular speed. In which of the following choices of axis of rotation will the kinetic energy of the plate be the largest?

Vedclass Test Series

Exam Paper Generator

Online Exam Module