Properties of Solids & Fluids · JEE Main previous year questions

2023 34 questions

1. Q332023 · 13 Apr 2023 · Shift 2

   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
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   Answer: B

2. Q382023 · 12 Apr 2023 · Shift 1

   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.$\frac{6}{5}$
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   Answer: A

3. Q552023 · 12 Apr 2023 · Shift 1· Numerical answer

   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 _________.

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   Answer: 4

4. Q532023 · 11 Apr 2023 · Shift 2· Numerical answer

   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 $\pi =22/7$)

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   Answer: 264

5. Q542023 · 11 Apr 2023 · Shift 2· Numerical answer

   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 _________ $\text{Hz}$.

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   Answer: 80

6. Q332023 · 10 Apr 2023 · Shift 1

   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
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   Answer: D

7. Q592023 · 10 Apr 2023 · Shift 1· Numerical answer
   
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   Answer: 20

8. Q582023 · 10 Apr 2023 · Shift 2· Numerical answer
   
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   Answer: 80

9. Q312023 · 8 Apr 2023 · Shift 1

   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.$5{\text{ cm}}^3$
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   Answer: D

10. Q442023 · 8 Apr 2023 · Shift 1

    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.$8400$
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    Answer: A

11. Q532023 · 8 Apr 2023 · Shift 1· Numerical answer

    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 $=1.6\times 10^{-19}\text{C}$ ).

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    Answer: 25

12. Q582023 · 8 Apr 2023 · Shift 1· Numerical answer

    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, $g=10{\text{ ms}}^{-2}$ ).

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    Answer: 10

13. Q312023 · 8 Apr 2023 · Shift 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.$2\times 10^{+6}\text{ Pa}$
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    Answer: D

14. Q362023 · 6 Apr 2023 · Shift 1

    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.$F=Mg(1\pm \rho {\rho }_0)$
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    Answer: A

15. Q532023 · 6 Apr 2023 · Shift 1· Numerical answer

    A steel rod has a radius of $20\text{ mm}$ and a length of $2.0\text{ m}$. A force of $62.8\text{ kN}$ stretches it along its length. Young's modulus of steel is $2.0\times 10^{11}{\text{ N/m}}^2$. The longitudinal strain produced in the wire is ________ $\times 10^{-5}$

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    Answer: 25

16. Q552023 · 6 Apr 2023 · Shift 1· Numerical answer

    A pole is vertically submerged in swimming pool, such that it gives a length of shadow $2.15\text{ m}$ within water when sunlight is incident at angle of $30^{\circ }$ with the surface of water. If swimming pool is filled to a height of $1.5\text{ m}$, then the height of the pole above the water surface in centimeters is ($n_w=4/3$) ________.

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    Answer: 50

17. Q362023 · 6 Apr 2023 · Shift 2

    Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below

    1. A.Both A and R are correct but R is NOT the correct explanation of A
    2. B.A is not correct but R is correct
    3. C.A is correct but R is not correct
    4. D.Both A and B are correct and R is the correct explanation of A
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    Answer: D

18. Q582023 · 6 Apr 2023 · Shift 2· Numerical answer

    A metal block of mass $\text{m}$ is suspended from a rigid support through a metal wire of diameter $14\text{ mm}$. The tensile stress developed in the wire under equilibrium state is $7\times 10^5{\text{Nm}}^{-2}$. The value of mass $\text{m}$ is _________ $\text{kg}$. (Take, $\text{g}=9.8{\text{ ms}}^{-2}$ and $\pi =\frac{22}{7}$ )

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    Answer: 11

19. Q492023 · 1 Feb 2023 · Shift 1

    A mercury drop of radius $10^{-3}\text{ m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45{\text{ Nm}}^{-1}$. The gain in surface energy is :

    1. A.$28\times 10^{-5}\text{ J}$
    2. B.$17.5\times 10^{-5}\text{ J}$
    3. C.$5\times 10^{-5}\text{ J}$
    4. D.$2.26\times 10^{-5}\text{ J}$
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    Answer: D

20. Q592023 · 1 Feb 2023 · Shift 1· Numerical answer

    A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ________.

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    Answer: 1

21. Q432023 · 31 Jan 2023 · Shift 1

    If 1000 droplets of water of surface tension $0.07\text{ N/m}$, having same radius $1\text{ mm}$ each, combine to form a single drop. In the process the released surface energy is :- $\left(\text{Take }\pi =\frac{22}{7}\right)$

    1. A.$7.92\times 10^{-4}\text{ J}$
    2. B.$7.92\times 10^{-6}\text{ J}$
    3. C.$8.8\times 10^{-5}\text{ J}$
    4. D.$9.68\times 10^{-4}\text{ J}$
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    Answer: A

22. Q452023 · 31 Jan 2023 · Shift 2

    Under the same load, wire A having length $5.0\text{ m}$ and cross section $2.5\times 10^{-5}{\text{ m}}^2$ stretches uniformly by the same amount as another wire B of length $6.0\text{ m}$ and a cross section of $3.0\times 10^{-5}{\text{ m}}^2$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be :

    1. A.$1:2$
    2. B.$1:4$
    3. C.$1:1$
    4. D.$1:10$
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    Answer: C

23. Q322023 · 30 Jan 2023 · Shift 1

    The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $5\mathrm{cm}$. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be ____ $\mathrm{m}$.

    1. A.$0.05$
    2. B.$0.20$
    3. C.$0.5$
    4. D.$0.10$
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    Answer: A

24. Q342023 · 30 Jan 2023 · Shift 1

    Choose the correct relationship between Poisson ratio ($\sigma$), bulk modulus ($\mathrm{K}$) and modulus of rigidity ($\eta$) of a given solid object :

    1. A.$\sigma =\frac{3K+2\eta }{6K+2\eta }$
    2. B.$\sigma =\frac{3K-2\eta }{6K+2\eta }$
    3. C.$\sigma =\frac{6K+2\eta }{3K-2\eta }$
    4. D.$\sigma =\frac{6K-2\eta }{3K-2\eta }$
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    Answer: B

25. Q352023 · 30 Jan 2023 · Shift 1

    The pressure $(\mathrm{P})$ and temperature $(\mathrm{T})$ relationship of an ideal gas obeys the equation ${\mathrm{PT}}^2=\mathrm{constant}$. The volume expansion coefficient of the gas will be :

    1. A.$3T^2$
    2. B.$\frac{3}{T^2}$
    3. C.$\frac{3}{T^3}$
    4. D.$\frac{3}{T}$
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    Answer: D