Properties of Solids & Fluids · JEE Main previous year questions

A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity '$v$'. Another ball of the same mass but of radius $2r$, falling through the same viscous medium will have terminal velocity:

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

Two blocks of mass $2\mathrm{kg}$ and $4\mathrm{kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0\times 10^{-5}\mathrm{m}$ and Young's modulus of the metal is $2.0\times 10^{11}N/{\mathrm{m}}^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi }$. The value of $\alpha$ is ____. [Use $g=10m/{\mathrm{s}}^2$]

Young's modulus of material of a wire of length '$L$' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's modulus will be :

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

Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

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

Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains $1\text{ g}$ of hydrogen and $B$ contains $1\text{ g}$ of oxygen. ${\text{P}}_{\text{A}}$ and ${\text{P}}_{\text{B}}$ are the pressures of the gases in A and B respectively, then $\frac{{\text{P}}_{\text{A}}}{{\text{P}}_{\text{B}}}$ is:

1. A.$4$
2. B.$32$
3. C.$8$
4. D.$16$

A small liquid drop of radius $R$ is divided into 27 identical liquid drops. If the surface tension is $T$, then the work done in the process will be:

1. A.$4\pi R^2\text{ T}$
2. B.$8\pi R^2\text{ T}$
3. C.$\frac{1}{8}\pi R^{2}T$
4. D.$3\pi R^2\text{ T}$

A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

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

Given below are two statements : Statement (I) :Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.Statement I is correct but statement II is incorrect
2. B.Statement I is incorrect but Statement II is correct
3. C.Both Statement I and Statement II are incorrect
4. D.Both Statement I and Statement II are correct

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2\times 10^9{\text{ Nm}}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is _______ (Given, $g=10{\text{ ms}}^{-2},\rho =1000{\text{ kg m}}^{-3}$)

The reading of pressure metre attached with a closed pipe is $4.5\times 10^4{\text{ N/m}}^2$. On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0\times 10^4{\text{ N/m}}^2$. The velocity of water is found to be $\sqrt{V}\text{ m/s}$. The value of $V$ is _______.

In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=\mathrm{R}T$, $X$ is pressure, $Y$ is volume, $\mathrm{R}$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

1. A.Impulse
2. B.Energy
3. C.Pressure gradient
4. D.Coefficient of viscosity

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is $12\text{ cm}$. When viewed from the opposite side, the apparent distance of the bubble is observed as $4\text{ cm}$. If the side of the ice cube is $24\text{ cm}$, the refractive index of the ice cube is

1. A.$\frac{3}{2}$
2. B.$\frac{4}{3}$
3. C.$\frac{2}{3}$
4. D.$\frac{6}{5}$

Glycerin of density $1.25\times 10^3{\text{ kg m}}^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are $10{\text{ cm}}^2$ and $5{\text{ cm}}^2$ and pressure drop across its length is $3{\text{ Nm}}^{-2}$. The rate of flow of glycerin through the pipe is $x\times 10^{-5}{\text{ m}}^3{\text{ s}}^{-1}$. The value of $x$ is _________.

The surface tension of soap solution is $3.5\times 10^{-2}{\text{ Nm}}^{-1}$. The amount of work done required to increase the radius of soap bubble from $10\text{ cm}$ to $20\text{ cm}$ is ________ $\times 10^{-4}\text{ J}$. (take $\pi =22/7$)

A wire of density $8\times 10^3{\text{ kg/m}}^3$ is stretched between two clamps $0.5\text{ m}$ apart. The extension developed in the wire is $3.2\times 10^{-4}\text{ m}$. If $Y=8\times 10^{10}{\text{ N/m}}^2$, the fundamental frequency of vibration in the wire will be _________ $\text{Hz}$.

Given below are two statements: Statement I : Pressure in a reservoir of water is same at all points at the same level of water. Statement II : The pressure applied to enclosed water is transmitted in all directions equally. In the light of the above statements, choose the correct answer from the options given below:

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

An air bubble of volume $1{\text{ cm}}^3$ rises from the bottom of a lake $40\text{ m}$ deep to the surface at a temperature of $12^{\circ }\text{C}$. The atmospheric pressure is $1\times 10^5\text{ Pa}$ the density of water is $1000{\text{ kg/m}}^3$ and $g=10{\text{ m/s}}^2$. There is no difference of the temperature of water at the depth of $40\text{ m}$ and on the surface. The volume of air bubble when it reaches the surface will be:

1. A.$4{\text{ cm}}^3$
2. B.$3{\text{ cm}}^3$
3. C.$2{\text{ cm}}^3$
4. D.$5{\text{ cm}}^3$

An aluminium rod with Young's modulus $Y=7.0\times 10^{10}{\text{ N/m}}^2$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in SI unit is:

1. A.$5600$
2. B.$2800$
3. C.$11200$
4. D.$8400$

A current of $2\text{ A}$ flows through a wire of cross-sectional area $25.0{\text{ mm}}^2$. The number of free electrons in a cubic meter are $2.0\times 10^{28}$. The drift velocity of the electrons is ___________ $\times 10^{-6}{\text{ ms}}^{-1}$ (given, charge on electron $=1.6\times 10^{-19}\text{C}$ ).

An air bubble of diameter $6\text{ mm}$ rises steadily through a solution of density $1750{\text{ kg/m}}^3$ at the rate of $0.35\text{ cm/s}$. The co-efficient of viscosity of the solution (neglect density of air) is ___________ $\text{Pas}$ (given, $g=10{\text{ ms}}^{-2}$ ).

A hydraulic automobile lift is designed to lift vehicles of mass $5000\text{ kg}$. The area of cross section of the cylinder carrying the load is $250{\text{ cm}}^2$. The maximum pressure the smaller piston would have to bear is [ Assume $g=10{\text{ m/s}}^2$ ]

1. A.$20\times 10^{+6}\text{ Pa}$
2. B.$200\times 10^{+6}\text{ Pa}$
3. C.$2\times 10^{+5}\text{ Pa}$
4. D.$2\times 10^{+6}\text{ Pa}$

A small ball of mass $\text{M}$ and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

1. A.$\text{F}=\text{Mg}\left(1-\frac{{\rho }_0}{\rho }\right)$
2. B.$\text{F}=\text{Mg}\left(1+\frac{\rho }{{\rho }_0}\right)$
3. C.$\text{F}=\text{Mg}\left(1+\frac{{\rho }_0}{\rho }\right)$
4. D.$F=Mg(1\pm \rho {\rho }_0)$