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 person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the options given below the lists.

A glass capillary tube is of the shape of truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is $\rho$, and its contact angle with glass is $\theta$, the value of h will be (g is the acceleration due to gravity)

If the piston is pushed at a speed of 5 mm s^$-$1, the air comes out of the nozzle with a speed of

If the density of air is $\rho$_a and that of the liquid $\rho$_l, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from left to right through the blocks. Then, in steady-state

Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density d_F. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

After the drop detaches, its surface energy is

If the radius of the opening of the dropper is $r$, the vertical force due to the surface tension on the drop of radius R (assuming $r$ << R) is

If r = 5 $ \times $ 10⁻⁴ m, $\rho $ = 10³ kg m⁻³ , g = 10 m/s² , T = 0.11 Nm⁻¹ , the radius of the drop when it detaches from the dropper is approximately

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

STATEMENT - 1 :

The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT - 2 :

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

When the gas bubble is at a height y from the bottom, its temperature is :

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is P. Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.

If the level of liquid starts decreasing slowly when the level of liquid is at a height $h_1$ above the cylinder, the block just starts moving up. Then, the value of $h_1$ is:

Let the cylinder is prevented from moving up, by applying a force and water level is further decreased. Then, the height of water level ( $h_2$ in the figure) for which the cylinder remains in original position without application of force is

If the height $h_2$ of water level is further decreased, then

A U-tube is rotated about one of its limbs with an angular velocity $\omega$. Find the difference in height $\mathrm{H}$ of the liquid (density $\rho$ ) level, where the diameter of the tube is $d < <\mathrm{L}$.