Properties of Solids & Fluids · JEE Main previous year questions

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

A small metallic sphere of diameter 2 mm and density $10.5{\text{ g/cm}}^3$ is dropped in glycerine having viscosity 10 Poise and density $1.5{\text{ g/cm}}^3$ respectively. The terminal velocity attained by the sphere is _____ cm/s. ($\pi =\frac{22}{7}$ and $g=10{\text{ m/s}}^2$)

1. A.1.0
2. B.1.5
3. C.3.0
4. D.2.0

An air bubble of volume $2.9{\text{ cm}}^3$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^{\circ }\text{C}$. The volume of the bubble when it reaches the surface, where the water temperature is $27^{\circ }\text{C}$, is _____ ${\text{cm}}^3$. ($g=10{\text{ m/s}}^2$, density of water $=10^3{\text{ kg/m}}^3$, and 1 atm pressure is $10^5\text{ Pa}$ )

1. A.2.0
2. B.4.2
3. C.3.0
4. D.4.5

A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t=A{\rho }^a{r}^b{\eta }^c{\sigma }^d$, where $A$ is a constant and $a,b,c$ and $d$ are integers. The value of $\frac{b+c}{a+d}$ is _____.

Given below are two statements : Statement I : Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II : Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below

1. A.Statement I is false but Statement II is true
2. B.Statement I is true but Statement II is false
3. C.Both Statement I and Statement II are false
4. D.Both Statement I and Statement II are true

Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1>r_2$. The measured liquid heights in these tubes are $h_1$ and $h_2$ respectively. [Ignore the weight of the liquid above the lowest point of miniscus]. The heights $h_1$ and $h_2$ and surface tensions $T_1$ and $T_2$ satisfy the relation :

1. A.$h_1>h_2$ and $T_1=T_2$
2. B.$h_1<h_2$ and $T_1=T_2$
3. C.$h_1>h_2$ and $T_1<T_2$
4. D.$h_1=h_2$ and $T_1=T_2$

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20cm/s$. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ____ $cm/s$.

A $3\mathrm{m}$ long wire of radius $3\mathrm{mm}$ shows an extension of $0.1\mathrm{mm}$ when loaded vertically by a mass of $50\mathrm{kg}$ in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P\times 10^{11}{\mathrm{Nm}}^{-2}$, where the value of $P$ is: (Take $g=3\pi {m/s}^2$)

1. A.$2.5$
2. B.$25$
3. C.$10$
4. D.$5$

Two liquids $A$ and $B$ have ${\theta }_A$ and ${\theta }_B$ as contact angles in a capillary tube. If $K=\cos {\theta }_A/\cos {\theta }_B$, then identify the correct statement:

1. A.K is negative, then liquid A and liquid B have convex meniscus.
2. B.$K$ is negative, then liquid $A$ and liquid $B$ have concave meniscus.
3. C.K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.
4. D.K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2=2d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is ${\theta }_2=2{\theta }_1$. If the shear moduli of material 1 is $4\times 10^{9}N/{\mathrm{m}}^2$, then shear moduli of material 2 is $x\times 10^{9}N/{\mathrm{m}}^2$, where value of $x$ is ____.

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa ).

1. A.24
2. B.4.4
3. C.18
4. D.6

During the melting of a slab of ice at 273 K at atmospheric pressure :

1. A.Internal energy of ice-water system remains unchanged.
2. B.Positive work is done by the ice-water system on the atmosphere.
3. C.Positive work is done on the ice-water system by the atmosphere.
4. D.Internal energy of the ice-water system decreases.

The radiation pressure exerted by a $450\mathrm{W}$ light source on a perfectly reflecting surface placed at $2\mathrm{m}$ away from it, is

1. A.$3\times 10^{-8}\text{Pascals}$
2. B.0
3. C.$1.5\times 10^{-8}\text{Pascals}$
4. D.$6\times 10^{-8}\text{Pascals}$

A solid steel ball of diameter $3.6\mathrm{mm}$ acquired terminal velocity $2.45\times 10^{-2}m/s$ while falling under gravity through an oil of density $925{\mathrm{kg}\mathrm{m}}^{-3}$. Take density of steel as $7825{\mathrm{kg}\mathrm{m}}^{-3}$ and $g$ as $9.8{m/s}^2$. The viscosity of the oil in SI unit is

1. A.$2.18$
2. B.$1.68$
3. C.$2.38$
4. D.$1.99$

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble $B$, then the value of $n$ is__________.

Match List I with List II. | List - I | List - II | | :--- | :--- | | (A) Coefficient of viscosity | (I) $\left[{\mathrm{ML}}^0{\mathrm{T}}^{-3}\right]$ | | (B) Intensity of wave | (II) $\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}\right]$ | | (C) Pressure gradient | (III) $\left[{\mathrm{M}}^{-1}{\mathrm{LT}}^2\right]$ | | (D) Compressibility | (IV) $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}\right]$ | Choose the correct answer from the options given below:

1. A.(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
2. B.(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
3. C.(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
4. D.(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

A steel wire of length $2\text{ m}$ and Young's modulus $2.0\times 10^{11}{\text{ N m}}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are $0.2$ and $10^{-3}$ respectively, then the elastic potential energy density of the wire is _________ $\times 10^5$ (in SI units).

Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :

1. A.$4\pi r^2\mathrm{T}\left[2-2^{1/3}\right]$
2. B.$4\pi r^2\mathrm{T}[1+\sqrt{2}]$
3. C.$4\pi r^2\mathrm{T}\left[2-2^{2/3}\right]$
4. D.$4\pi r^2\mathrm{T}[\sqrt{2}-1]$

The internal energy of air in $4\mathrm{m}\times 4\mathrm{m}\times 3\mathrm{m}$ sized room at 1 atmospheric pressure will be ____ $\times 10^6\mathrm{J}$ (Consider air as diatomic molecule)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below

1. A.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
2. B.$\mathbf{A}$ is false but $\mathbf{R}$ is true
3. C.$\mathbf{A}$ is true but $\mathbf{R}$ is false
4. D.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$

In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of $\eta$ will change. Choose the correct answer from the options given below:

1. A.C, D and E Only
2. B.A, B and E Only
3. C.A, C and D Only
4. D.B, D and E Only

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

1. A.B, C, D Only
2. B.C, D, E Only
3. C.A, D, E Only
4. D.A, B, C Only

An air bubble of radius $0.1\mathrm{cm}$ lies at a depth of $20\mathrm{cm}$ below the free surface of a liquid of density $1000kg/{\mathrm{m}}^3$. If the pressure inside the bubble is $2100N/{\mathrm{m}}^2$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use $g=10m/{\mathrm{s}}^2$ )

1. A.$0.02$
2. B.$0.05$
3. C.$0.25$
4. D.$0.1$

The temperature of $1\mathrm{mole}$ of an ideal monoatomic gas is increased by $50^{\circ }\mathrm{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2}=\frac{x}{9}$ then the value of $x$ is ____.

The increase in pressure required to decrease the volume of a water sample by $0.2\%$ is $\mathrm{P}\times 10^5{\mathrm{Nm}}^{-2}$. Bulk modulus of water is $2.15\times 10^9{\mathrm{Nm}}^{-2}$. The value of P is ________ .