1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=$ $\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a 1}$, the radius of the bubble is found to be $r_{1}$ and the temperature of the enclosed gas is $T_{1}$. When the atmospheric pressure is $P_{a 2}$, the radius of the bubble and the temperature of the enclosed gas are $r_{2}$ and $T_{2}$, respectively.

Which of the following statement(s) is(are) correct?
A
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{r_{1}}{r_{2}}\right)^{5}=\frac{P_{a 2}+\frac{2 S}{r_{2}}}{P_{a 1}+\frac{2 S}{r_{1}}}$.
B
If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure.
C
If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then $\left(\frac{r_{1}}{r_{2}}\right)^{3}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}$.
D
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{T_{2}}{T_{1}}\right)^{\frac{5}{2}}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}$.
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

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 $0.05 \mathrm{~kg} \mathrm{~m}^{-3}$.
3
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
4
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
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