MHTCET 16 May 2024 Shift 1 Paper

Concept:Capillary rise is governed by the balance of surface tension and hydrostatic pressure.When the tube length above water is reduced, the rise adjusts and the apparent contact angle changes.Explanation:The capillary rise formula is $h = \frac{2T\cos\theta}{r\rho g}$.Initially, $\theta = 0^\circ$ and rise is $h$.So, $h = \frac{2T\cos 0^\circ}{r\rho g}$.When the tube is depressed, the available height above water becomes $\frac{h}{3}$.Hence the new rise is $h' = \frac{h}{3}$, and the new contact angle is $\theta'$.Using the same formula, $h' = \frac{2T\cos\theta'}{r\rho g}$.Dividing the two equations, we get $\frac{h'}{h} = \frac{\cos\theta'}{\cos 0^\circ}$.Substituting values, $\frac{1}{3} = \frac{\cos\theta'}{1}$.Therefore, $\cos\theta' = \frac{1}{3}$.So, the new apparent angle of contact is $\theta' = \cos^{-1}\left(\frac{1}{3}\right)$.Answer:$\cos^{-1}\left(\frac{1}{3}\right)$Hence, the correct option is B.