$y = \frac{a}{2}$
$ \Rightarrow \frac{a}{2} = a\sin (\omega \,t + {\phi _0})$
$ \Rightarrow (\omega \,t + {\phi _0}) = \phi = \frac{\pi }{6}$ or $\frac{{5\pi }}{6}$
Physical meaning of $\phi = \frac{\pi }{6}$ : Particle is at point $P$ and it is going towards B
Physical meaning of $\phi = \frac{{5\pi }}{6}$ : Particle is at point $P$ and it is going towards $O$
So phase difference $\Delta \phi = \frac{{5\pi }}{6} - \frac{\pi }{6} = \frac{{2\pi }}{3} = 120^\circ $
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[Take $\left.\varepsilon_{0}=8.85 \times 10^{-12} \,{F} / {m}\right]$
$(I)$ The average speed of molecules is larger than root mean square speed.
$(II)$ Mean free path of molecules is larger than the mean distance between molecules.
$(III)$ Mean free path of molecules increases with temperature.
$(IV)$ The rms speed of nitrogen is smaller than oxygen molecule.
Which of the above statements are correct?