Let M and L be the mass and length of a thin | vedclass

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

Question

(A) The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to its length is

Vedclass · Accepted Answer

$1: 2$

Vedclass · Answer

(A) The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to its length is $I_1 = \frac{ML^2}{12}$.By definition,$I_1 = MK_1^2$,where $K_1$ is the radius of gyration.So,$MK_1^2 = \frac{ML^2}{12} \implies K_1 = \frac{L}{\sqrt{12}} = \frac{L}{2\sqrt{3}}$.The moment of inertia about an axis passing through one end and perpendicular to its length is $I_2 = \frac{ML^2}{3}$.By definition,$I_2 = MK_2^2$,where $K_2$ is the radius of gyration.So,$MK_2^2 = \frac{ML^2}{3} \implies K_2 = \frac{L}{\sqrt{3}}$.The ratio of the radius of gyration in the first case to the second case is $\frac{K_1}{K_2} = \frac{L / (2\sqrt{3})}{L / \sqrt{3}} = \frac{1}{2}$.Thus,the ratio is $1:2$.

Similar Questions

Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. Their moments of inertia about their diameters are $I_A$ and $I_B$ respectively. Which of the following relations is correct?

The moment of inertia of a solid cylinder of mass $20 \ kg$,length $1 \ m$,and radius $0.2 \ m$ about its geometric axis is (in $kg \cdot m^2$):

$A$ thin rod of mass $M$ and length $L$ is bent at its midpoint $A$ such that it forms an angle of $60^{\circ}$. What is the moment of inertia about an axis passing through the midpoint $A$ and perpendicular to the plane of the rod?

The moment of inertia of a uniform annular disc of internal radius $r$,external radius $R$,and mass $M$ about an axis passing through its centre and perpendicular to its plane is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module