A body is rotating about its own axis. Its rotational kinetic energy is ' $x$ ' and its angular momentum is…
A body is rotating about its own axis. Its rotational kinetic energy is ' $x$ ' and its angular momentum is ' $y$ '. Hence its moment of inertia about the axis is
$\frac{x^2}{2 y}$
$\frac{y}{2 x}$
$\frac{x}{2 y}$
$\frac{y^2}{2 x}$
Solution
The kinetic energy of a rotating body is given by $x=\frac{I \omega^2}{2}$ and the angular momentum is given by $\mathrm{y}=\mathrm{I} \omega$, where $\mathrm{I}$ is the moment of inertia, $\omega$ the angular velocity.
Therefore, we can write,
$\mathrm{y}^2=2 \mathrm{I}\left(\frac{\mathrm{I} \omega^2}{2}\right)=2 \mathrm{Ix}$
On re-writing,
$I=\frac{y^2}{2 x}$