Angle of Contact & Capillarity question from MHT CET 2024 (16 May, Shift 1)

Answer: (b)

1. $h = \frac{2T\cos\theta}{r\rho g}$, so for the same tube and liquid $h \propto \cos\theta$; with $\theta = 0$ the full rise is $h$.
2. If only $\frac{h}{3}$ of tube is above water, the meniscus adjusts so that $\cos\theta' = \frac{h/3}{h} = \frac{1}{3}$.
3. So the answer is (b) $\cos^{-1}\left(\frac{1}{3}\right)$.