An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$ $0.8 \mathrm{~kg} \mathrm{~s}^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_{1}=0.1 \mathrm{~m}^{2}$ and the upper end is $A_{2}=0.4 \mathrm{~m}^{2}$. The pressure and the temperature of the gas at the lower end are $600 \mathrm{~Pa}$ and $300 \mathrm{~K}$, respectively, while its temperature at the upper end is $150 \mathrm{~K}$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure.
Which of the following statement(s) is(are) correct?
A
The pressure of the gas at the upper end of the chimney is $300 \mathrm{~Pa}$.
B
The velocity of the gas at the lower end of the chimney is $40 \mathrm{~m} \mathrm{~s}^{-1}$ and at the upper end is $20 \mathrm{~ms}^{-1}$.
C
The height of the chimney is $590 \mathrm{~m}$.
D
The density of the gas at the upper end is $0.05 \mathrm{~kg} \mathrm{~m}^{-3}$.
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $$\theta$$ = 45$$^\circ$$. P1 and P2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let $$\beta$$ = (P1 $$-$$ P2)/($$\rho$$gd), where $$\rho$$ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?
A
$$\beta$$ = 0 when a = g/$$\sqrt 2 $$
B
$$\beta$$ > 0 when a = g/$$\sqrt 2 $$
C
$$\beta = {{\sqrt 2 - 1} \over {\sqrt 2 }}$$ when a = g/2
D
$$\beta = {1 \over {\sqrt 2 }}$$ when a = g/2
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
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
4
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).
