Question

A wire of mass $5\text{kg}$ and length $3.5\text{m}$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is

• A. $3.1{\text{kg-m}}^2$
• B. $2.58{\text{kg-m}}^2$
• C. $0.77{\text{kg-m}}^2$
• D. $1.55{\text{kg-m}}^2$

Answer 1

The correct option is D $1.55{\text{kg-m}}^2$

Given, length of wire $l=2.5\text{m}$
& mass of wire $m=5\text{kg}$

Let the wire bent in focus of a circular ring of radius $r$
So, radius of ring $r=\frac{l}{2\pi }$

The moment of inertia of the ring about its axis
$I=m{r}^2=m{\left(\frac{l}{2\pi }\right)}^2=\frac{m{l}^2}{4{\pi }^2}$
$I=\frac{5\times (3.5{)}^2}{4\times {\pi }^2}=1.55{\text{kg-m}}^2$
$I=1.55{\text{kg-m}}^2$