Question

Moment of inertia of a uniform solid cylinder of radius $1\text{m}$ about its central axis is $1{\text{kg-m}}^2$. The moment of inertia of a uniform solid cylinder of the same mass, but of radius $2\text{m}$ about its central axis is (in ${\text{kg-m}}^2$)

(in ${\text{kg.m}}^{-2}$)

Answer 1

Given,
Radius of solid cylinder $1\left(r_1\right)=1\text{m}$
Moment of inertia about central axis $\left(I_1\right)=1{\text{kg-m}}^2$
Radius of solid cylinder $2\left(r_2\right)=2\text{m}$
We know that
$I_1=\frac{m{r}_1^2}{2}$
$\Rightarrow m=2\text{kg}$
$\therefore$ Moment of inertia of solid cylinder $2$ about central axis $\left(I_2\right)=\frac{m{r}_2^2}{2}$
$=\frac{2\times (2{)}^2}{2}=4{\text{kg-m}}^2$