A body executes pure rotation. The angular velocity ω of the body,...

For a rigid body executing pure rotation, all particles of the body rotate with the same angular velocity $\omega$.

The linear speed $v$ of a particle at a distance $r$ from the axis of rotation is given by $v = \omega r$.

Since $\omega$ is the same for all particles of the rigid body, it does not depend on the distance $r$ of the particle from the axis of rotation.

Therefore, $\omega$ is independent of $r$.