Properties of Matter · Physics · JEE Advanced
MCQ (More than One Correct Answer)
A table tennis ball has radius $(3 / 2) \times 10^{-2} \mathrm{~m}$ and mass $(22 / 7) \times 10^{-3} \mathrm{~kg}$. It is slowly pushed down into a swimming pool to a depth of $d=0.7 \mathrm{~m}$ below the water surface and then released from rest. It emerges from the water surface at speed $v$, without getting wet, and rises up to a height $H$. Which of the following option(s) is(are) correct?
[Given: $\pi=22 / 7, g=10 \mathrm{~m} \mathrm{~s}^{-2}$, density of water $=1 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, viscosity of water $=1 \times 10^{-3} \mathrm{~Pa}$-s.]
Which of the following statement(s) is(are) correct?
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?
Which of the following options is / are correct?
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 dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
Numerical
[Given: Surface tension of the liquid is $0.075 \mathrm{~N} \mathrm{~m}^{-1}$, atmospheric pressure is $10^5 \mathrm{~N} \mathrm{~m}^{-2}$, acceleration due to gravity $(\mathrm{g})$ is $10 \mathrm{~m} \mathrm{~s}^{-2}$, density of the liquid is $10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and contact angle of capillary surface with the liquid is zero]
$$\rho \left( h \right) = {\rho _0}{e^{ - {h \over {{h_0}}}}}$$, where $$\rho $$0 = 1.25 kg m−3 and h0 = 6000 m, the value of N is _________.
p0 - p = $${7 \over {2N}}\rho v_t^2$$. The value of 𝑁 is ________.
due to gravity are 103 kg m−3 , 0.07 Nm−1 and 10 ms−2 , respectively, the value of h (in mm) is _________.
[Young's modulus for copper and steel are 1 $$ \times $$ 1011 N/m2 and 2 $$ \times $$ 1011 N/m2 respectively.]
[Neglect the heat exchange with surrounding]
Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m$$^2$$. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio $$n_B/n_A$$, where $$n_A$$ and $$n_B$$ are the number of moles of air in bubbles A and B, respectively. (Neglect the effect of gravity.)
A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. (Take atmospheric pressure = 1.0 $$\times$$ 10$$^5$$ N/m$$^2$$, density of water = 1000 kg/m$$^3$$ and g = 10 m/s$$^2$$. Neglect any effect of surface tension.)
MCQ (Single Correct Answer)
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.
| List - I | List - II |
|---|---|
| P. Lift is accelerating vertically up. | 1. d=1.2 m |
| Q. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration. |
2. d > 1.02 m |
| R. Lift is moving vertically up with constant speed. |
3. d < 1.2 m |
| S. Lift is falling freely. | 4. No water leaks out of the jar |
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
After the drop detaches, its surface energy 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
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
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.
| Column I | Column II | ||
|---|---|---|---|
| (A) | Bimetallic strip | (P) | Radiation from a hot body |
| (B) | Steam engine | (Q) | Energy conversion |
| (C) | Incandescent lamp | (R) | Melting |
| (D) | Electric fuse | (S) | Thermal expansion |