Physics - Rotation Question with Solution | TestHub

The moment of inertia of the system about the axis of the paraboloid is $\mathrm{I}=4\mathrm{ma}\left({\mathrm{y}}_1+{\mathrm{y}}_2+{\mathrm{y}}_3\right)$.

If potential energy at O is taken to be zero, the potential energy of the system is $\mathrm{mg}\left({\mathrm{y}}_1+{\mathrm{y}}_2+{\mathrm{y}}_3\right)$.

If the particle at $\left({\mathrm{x}}_1,{\mathrm{y}}_1,{\mathrm{z}}_1\right)$ slides down the smooth surface, its speed at O is $\sqrt{2{\mathrm{gy}}_1}$

If the paraboloid spins about OY with an angular speed $\omega$, the kinetic energy of the system will be ma $(\mathrm{y}+\mathrm{y}+\mathrm{y}){\omega }^2$.