Properties of Solids & Fluids · JEE Main previous year questions

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to $135^{\circ }$ and $0^{\circ }$, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius ${\mathrm{r}}_1$, while water rises by the same amount h in a capillary tube of radius ${\mathrm{r}}_2$. The ratio, $({\mathrm{r}}_1/{\mathrm{r}}_2)$, is then close to :

1. A.2/5
2. B.2/3
3. C.3/5
4. D.4/5

One mole of ideal gas passes through a process where pressure and volume obey the relation $P=P_0\left[1-\frac{1}{2}{\left(\frac{V_0}{V}\right)}^2\right]$. Here ${\mathrm{P}}_0$ and ${\mathrm{V}}_0$ are constants. Calculate the change in the temperature of the gas if its volume changes form ${\mathrm{V}}_0$ to $2{\mathrm{V}}_0$

1. A.$\frac{3}{4}\frac{P_0{V}_0}{R}$
2. B.$\frac{1}{2}\frac{P_0{V}_0}{R}$
3. C.$\frac{5}{4}\frac{P_0{V}_0}{R}$
4. D.$\frac{1}{4}\frac{P_0{V}_0}{R}$

Water from a tap emerges vertically downwards with an initial speed of $1.0\mathrm{m}{\mathrm{s}}^{-1}$ . The cross-sectional area of the tap is $10^{-4}{\mathrm{m}}^2$. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be : (Take $g=10\mathrm{m}{\mathrm{s}}^{-2}$)

1. A.$5\times 10^{-4}{\mathrm{m}}^2$
2. B.$2\times 10^{-5}{\mathrm{m}}^2$
3. C.$5\times 10^{-5}{\mathrm{m}}^2$
4. D.$1\times 10^{-5}{\mathrm{m}}^2$

A submarine experiences a pressure of $5.05\times 10^6\mathrm{Pa}$ at a depth of ${\mathrm{d}}_1$ in a sea. When it goes further to a depth of ${\mathrm{d}}_2$, it experiences a pressure of $8.08\times 10^6\mathrm{Pa}$. Then ${\mathrm{d}}_2-{\mathrm{d}}_1$ is approximately (density of water $=10^{3}kg/{\mathrm{m}}^3$ and acceleration due to gravity $=10\mathrm{m}{\mathrm{s}}^{-2}$ ) :

1. A.600 m
2. B.400 m
3. C.300 m
4. D.500 m

In an experiment, brass and steel wires of length 1 m each with areas of cross section $1\mathrm{m}{\mathrm{m}}^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, $120\times 10^{9}N/{\mathrm{m}}^2$ and $60\times 10^{9}N/{\mathrm{m}}^2$]

1. A.$8.0\times 10^{6}N/{\mathrm{m}}^2$
2. B.$1.2\times 10^{6}N/{\mathrm{m}}^2$
3. C.$0.2\times 10^{6}N/{\mathrm{m}}^2$
4. D.$1.8\times 10^{6}N/{\mathrm{m}}^2$

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = $10^{3}kg/{\mathrm{m}}^3$]

1. A.30.1 kg
2. B.87.5 kg
3. C.65.4 kg
4. D.46.3 kg

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta \mathrm{T}$. the heat required to produce the same change in temperature, at a constant pressure is :

1. A.$\frac{7}{5}Q$
2. B.$\frac{3}{2}Q$
3. C.$\frac{2}{3}Q$
4. D.$\frac{5}{3}Q$

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :

1. A.M
2. B.4M
3. C.M/2
4. D.2M

A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :-

1. A.0.8
2. B.0.7
3. C.0.6
4. D.0.5

An ideal gas occupies a volume of $2{\mathrm{m}}^3$ at a pressure of $3\times 10^6\mathrm{Pa}$. The energy of the gas is :

1. A.$6\times 10^4\mathrm{J}$
2. B.$9\times 10^6\mathrm{J}$
3. C.$3\times 10^2\mathrm{J}$
4. D.$10^8\mathrm{J}$

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:

1. A.5.0 mm
2. B.zero
3. C.3.0 mm
4. D.4.0 mm

1. A.
2. B.
3. C.
4. D.

Drift speed of electrons, when $1.5\text{ A}$ of current flows in a copper wire of cross section $5{\text{ mm}}^2$, is $v$. If the electron density in copper is $9\times 10^{28}/{\text{m}}^3$ the value of $v$ in mm/s is close to (Take charge of electron to be $=1.6\times 10^{-19}\text{C}$)

1. A.0.02
2. B.3
3. C.2
4. D.0.2

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let ${\text{P}}_2$ be the pressure inside the inner bubble and ${\text{P}}_0$, the pressure outside the outer bubble. Radius of another bubble with pressure difference ${\text{P}}_2-{\text{P}}_0$ between its inside and outside would be :

1. A.12 cm
2. B.2.4 cm
3. C.6 cm
4. D.4.8 cm

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left(\frac{dr}{r}\right)$ is:

1. A.$\frac{mg}{Ka}$
2. B.$\frac{Ka}{mg}$
3. C.$\frac{Ka}{3mg}$
4. D.$\frac{mg}{3Ka}$

The mass of a hydrogen molecule is $3.32\times 10^{-27}\mathrm{kg}$. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2\mathrm{c}{\mathrm{m}}^2$ at an angle of $45^{\circ }$ to the normal, and rebound elastically with a speed of $10^{3}m/s$, then the pressure on the wall is nearly:

1. A.$2.35\times 10^3\mathrm{N}{\mathrm{m}}^{-2}$
2. B.$4.70\times 10^3\mathrm{N}{\mathrm{m}}^{-2}$
3. C.$2.35\times 10^2\mathrm{N}{\mathrm{m}}^{-2}$
4. D.$4.70\times 10^2\mathrm{N}{\mathrm{m}}^{-2}$

A steel rail of length 5 m and area of cross section $40{\mathrm{cm}}^2$ is prevented from expanding along its length while the temperature rises by $10^{\circ }\mathrm{C}$. If coefficient of linear expansion and Young’s modulus of steel are $1.2\times 10^{-5}{\mathrm{K}}^{-1}$ and $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$ respectively, the force developed in the rail is approximately :

1. A.$2\times 10^7\mathrm{N}$
2. B.$1\times 10^5\mathrm{N}$
3. C.$2\times 10^9\mathrm{N}$
4. D.$3\times 10^{-5}\mathrm{N}$

Two tubes of radii $r_1$ and $r_2$, and lengths $l_1$ and $l_2$ , respectively, are connected in series and a liquid flows through each of them in stream line conditions. ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are pressure differences across the two tubes. If ${\mathrm{P}}_2$ is $4{\mathrm{P}}_1$ and $l_2$ is $\frac{l_1}{4}$ , then the radius $r_2$ will be equal to :

1. A.$r_1$
2. B.$2r_1$
3. C.$4r_1$
4. D.$\frac{r_1}{2}$

An open glass tube is immersed in mercury in such a way that a length of $8\mathrm{cm}$ extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional $46\mathrm{cm}$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $=76\mathrm{cm}$ of $\mathrm{Hg}$)

1. A.$16\mathrm{cm}$
2. B.$22\mathrm{cm}$
3. C.$38\mathrm{cm}$
4. D.$6\mathrm{cm}$

The pressure that has to be applied to the ends of a steel wire of length $10\mathrm{cm}$ to keep its length constant when its temperature is raised by $100^{\circ }\mathrm{C}$ is: (For steel Young's modulus is $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$ and coefficient of thermal expansion is $1.1\times 10^{-5}{\mathrm{K}}^{-1}$ )

1. A.$2.2\times 10^8\mathrm{Pa}$
2. B.$2.2\times 10^9\mathrm{Pa}$
3. C.$2.2\times 10^7\mathrm{Pa}$
4. D.$2.2\times 10^6\mathrm{Pa}$

1. A.$R^2\sqrt{\frac{{\rho }_{w}g}{3T}}$
2. B.$R^2\sqrt{\frac{{\rho }_{w}g}{6T}}$
3. C.$R^2\sqrt{\frac{{\rho }_{w}g}{T}}$
4. D.$R^2\sqrt{\frac{2{\rho }_{w}g}{3T}}$

The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to

1. A.$a^2$
2. B.$a^3$
3. C.$a$
4. D.$a^{-1}$

Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime }$ such that the ratio $A/A^{\prime }$ is 5. If the pressure difference of water between the two ends is $3\times 10^5\mathrm{N}{\mathrm{m}}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1. A.$5\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$10\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$25\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$50\sqrt{10}\mathrm{m}{\mathrm{s}}^{-1}$

A structural steel rod has a radius of $10\mathrm{mm}$ and length of $1.0\mathrm{m}$. A $100\mathrm{kN}$ force stretches it along its length. Young's modulus of structural steel is $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$. The percentage strain is about

1. A.$0.16\%$
2. B.$0.32\%$
3. C.$0.08\%$
4. D.$0.24\%$

A perfect gas at $27^{\circ }\mathrm{C}$ is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to

1. A.$327^{\circ }\mathrm{C}$
2. B.$200^{\circ }\mathrm{C}$
3. C.$54^{\circ }\mathrm{C}$
4. D.$300^{\circ }\mathrm{C}$