As shown schematically in the figure, two vessels contain water solutions (at temperature T) of
potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per
unit volume with $$\Delta $$n = (n1 − n2) << n1. When they are connected by a tube of small length l and
cross-sectional area S, KMnO4 starts to diffuse from the left to the right vessel through the tube.
Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial
pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the
viscous force −$$\beta $$v on each molecule, where $$\beta $$ is a constant. Neglecting all terms of the order ($$\Delta $$n)2,
which of the following is/are correct? (kB is the Boltzmann constant)
A
the force causing the molecules to move across the tube is $$\Delta n{k_b}TS$$
B
force balance implies $${n_1}\beta vl = \Delta n{k_B}T$$
C
total number of molecules going across the tube per sec is $$\left( {{{\Delta n} \over l}} \right)\left( {{{{k_B}T} \over \beta }} \right)S$$
D
rate of molecules getting transferred through the tube does not change with time
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0$$^\circ $$ and 60$$^\circ $$, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is (are) correct? [Surface tension of water = 0.075 N/m, density of water = 1000 kg/m3, take g = 10 m/s2]
A
For case I, if the joint is kept at 8 cm above the water surface, the height of water colomn in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus).
B
For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus).
C
The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.
D
For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus).
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$$ Which of the following statements is (are) true?
A
The resistive force of liquid on the plate is inversely proportional to $$h$$
B
The resistive force of liquid on the plate is independent of the area of the plate
C
The tangential (shear) stress on the floor of the tank increases with $${\mu _0}$$
D
The tangential (shear) stress on the plate varies linearly with the viscosity $$\eta $$ of the liquid
4
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A uniform capillary tube of inner radius $$r$$ is dipped vertically into a beaker filled with water. The water rises to a height $$h$$ in the capillary tube above the water surface in the beaker. The surface tension of water is $$\sigma .$$ The angle of contact between water and the wall of the capillary tube is $$\theta .$$ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
A
For a given material of the capillary tube, $$h$$ decreases with increase in $$r$$
B
For a given material of the capillary tube, $$h$$ is independent of $$\sigma $$
C
If this experiment is performed in a lift going up with a constant acceleration, then $$h$$ decreases
D
$$h$$ is proportional to contact angle $$\theta $$
