Properties of Solids & Fluids · JEE Main previous year questions

2022 28 questions

1. Q382022 · 29 Jul 2022 · Shift 1

   If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

   1. A.remain same
   2. B.become 8 times its initial value
   3. C.become $\frac{1}{4}$ of its initial value
   4. D.become 4 times its initial value
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   Answer: A

2. Q532022 · 29 Jul 2022 · Shift 2· Numerical answer

   A metal wire of length $0.5\mathrm{m}$ and cross-sectional area $10^{-4}{\mathrm{m}}^2$ has breaking stress $5\times 10^8\mathrm{N}{\mathrm{m}}^{-2}$. A block of $10\mathrm{kg}$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be ____ $\mathrm{m}{\mathrm{s}}^{-1}$.

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   Answer: 50

3. Q362022 · 28 Jul 2022 · Shift 1

   The force required to stretch a wire of cross-section $1{\text{ cm}}^2$ to double its length will be : (Given Young's modulus of the wire $=2\times 10^{11}{\text{ N/m}}^2$)

   1. A.$1\times 10^7\text{ N}$
   2. B.$1.5\times 10^7\text{ N}$
   3. C.$2\times 10^7\text{ N}$
   4. D.$2.5\times 10^7\text{ N}$
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   Answer: C

4. Q552022 · 28 Jul 2022 · Shift 1· Numerical answer

   The diameter of an air bubble which was initially $2\text{ mm}$, rises steadily through a solution of density $1750{\text{ kg m}}^{-3}$ at the rate of $0.35{\text{ cms}}^{-1}$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligible).

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   Answer: 11

5. Q332022 · 28 Jul 2022 · Shift 2

   A pressure-pump has a horizontal tube of cross sectional area $10{\text{ cm}}^2$ for the outflow of water at a speed of $20\text{ m/s}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is : [given: density of water $=1000{\text{ kg/m}}^3$]

   1. A.$300\text{ N}$
   2. B.$500\text{ N}$
   3. C.$250\text{ N}$
   4. D.$400\text{ N}$
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   Answer: D

6. Q392022 · 27 Jul 2022 · Shift 1

   Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be $1:4$. C. The ratio of pressure will be $1:1$. D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1:4$. Choose the correct answer from the options given below :

   1. A.A and C only
   2. B.B and D only
   3. C.A and B only
   4. D.C and D only
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   Answer: C

7. Q372022 · 27 Jul 2022 · Shift 2

   A steel wire of length $3.2\mathrm{m}$ $\left({\mathrm{Y}}_{\mathrm{s}}=2.0\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}\right)$ and a copper wire of length $4.4\mathrm{m}$ $\left({\mathrm{Y}}_{\mathrm{c}}=1.1\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}\right)$, both of radius $1.4\mathrm{mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\mathrm{mm}$. The load applied, in Newton, will be: ( Given $\pi =\frac{22}{7}$ )

   1. A.$360$
   2. B.$180$
   3. C.$1080$
   4. D.$154$
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   Answer: D

8. Q512022 · 27 Jul 2022 · Shift 2· Numerical answer
   
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   Answer: 2

9. Q582022 · 27 Jul 2022 · Shift 2· Numerical answer

   A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of another single soap bubble of radius r cm. The value of r is ___________.

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   Answer: 2

10. Q412022 · 26 Jul 2022 · Shift 1

    $7\mathrm{mol}$ of a certain monoatomic ideal gas undergoes a temperature increase of $40\mathrm{K}$ at constant pressure. The increase in the internal energy of the gas in this process is : (Given $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$ )

    1. A.$5810\mathrm{J}$
    2. B.$3486\mathrm{J}$
    3. C.$11620\mathrm{J}$
    4. D.$6972\mathrm{J}$
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    Answer: B

11. Q432022 · 26 Jul 2022 · Shift 1

    A water drop of radius $1\mathrm{cm}$ is broken into $729$ equal droplets. If surface tension of water is $75dyne/cm$, then the gain in surface energy upto first decimal place will be : (Given $\pi =3.14$ )

    1. A.$8.5\times 10^{-4}\mathrm{J}$
    2. B.$8.2\times 10^{-4}\mathrm{J}$
    3. C.$7.5\times 10^{-4}\mathrm{J}$
    4. D.$5.3\times 10^{-4}\mathrm{J}$
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    Answer: C

12. Q322022 · 25 Jul 2022 · Shift 2

    A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times 10^{-4}{\text{ Ncm}}^{-1}$. The radius of drop in $\mathrm{cm}$ will be : ($g=10{\text{ ms}}^{-2}$)

    1. A.$\frac{15}{\sqrt{(2\rho -\sigma )}}$
    2. B.$\frac{15}{\sqrt{(\rho -\sigma )}}$
    3. C.$\frac{3}{2\sqrt{(\rho -\sigma )}}$
    4. D.$\frac{3}{20\sqrt{(2\rho -\sigma )}}$
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    Answer: A

13. Q352022 · 30 Jun 2022 · Shift 1

    An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed v. The coefficient of viscosity of the solution is given by :

    1. A.$\eta =\frac{4r\sigma g}{9v}$
    2. B.$\eta =\frac{2r^2\sigma g}{9v}$
    3. C.$\eta =\frac{2\pi r^2\sigma g}{9v}$
    4. D.$\eta =\frac{2r^2\sigma g}{3\pi v}$
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    Answer: B

14. Q382022 · 30 Jun 2022 · Shift 1

    The pressure of the gas in a constant volume gas thermometer is $100\mathrm{cm}$ of mercury when placed in melting ice at $1\mathrm{atm}$. When the bulb is placed in a liquid, the pressure becomes $180\mathrm{cm}$ of mercury. Temperature of the liquid is : (Given $0^{\circ }\mathrm{C}=273\mathrm{K}$)

    1. A.$300\mathrm{K}$
    2. B.$400\mathrm{K}$
    3. C.$600\mathrm{K}$
    4. D.$491\mathrm{K}$
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    Answer: D

15. Q532022 · 30 Jun 2022 · Shift 1· Numerical answer

    The excess pressure inside a liquid drop is $500{\text{ Nm}}^{-2}$. If the radius of the drop is $2\text{ mm}$, the surface tension of liquid is $x\times 10^{-3}{\text{ Nm}}^{-1}$. The value of $x$ is ___________.

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    Answer: 500

16. Q372022 · 28 Jun 2022 · Shift 2

    A water drop of radius $1\mu \text{m}$ falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is $1.8\times 10^{-5}{\text{ Nsm}}^{-2}$ and its density is negligible as compared to that of water $10^6{\text{ gm}}^{-3}$. Terminal velocity of the water drop is : (Take acceleration due to gravity $=10{\text{ ms}}^{-2}$)

    1. A.$145.4\times 10^{-6}{\text{ ms}}^{-1}$
    2. B.$118.0\times 10^{-6}{\text{ ms}}^{-1}$
    3. C.$132.6\times 10^{-6}{\text{ ms}}^{-1}$
    4. D.$123.4\times 10^{-6}{\text{ ms}}^{-1}$
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    Answer: D

17. Q582022 · 28 Jun 2022 · Shift 2· Numerical answer

    A liquid of density $750\mathrm{kg}{\mathrm{m}}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from ${\mathrm{A}}_1=1.2\times 10^{-2}{\mathrm{m}}^2$ to ${\mathrm{A}}_2=\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4500\mathrm{Pa}$. The rate of flow of liquid is ____ $\times 10^{-3}{\mathrm{m}}^3{\mathrm{s}}^{-1}$.

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    Answer: 24

18. Q492022 · 27 Jun 2022 · Shift 1

    A mixture of hydrogen and oxygen has volume $2000\mathrm{c}{\mathrm{m}}^3$, temperature $300\mathrm{K}$, pressure $100\mathrm{kPa}$ and mass $0.76\mathrm{g}$. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be: [Take gas constant $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$]

    1. A.$\frac{1}{3}$
    2. B.$\frac{3}{1}$
    3. C.$\frac{1}{16}$
    4. D.$\frac{16}{1}$
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    Answer: B

19. Q542022 · 27 Jun 2022 · Shift 1· Numerical answer

    The current density in a cylindrical wire of radius $4\mathrm{mm}$ is $4\times 10^6\mathrm{A}{\mathrm{m}}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$ is ____ $\pi \mathrm{A}$.

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    Answer: 48

20. Q332022 · 27 Jun 2022 · Shift 2

    When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

    1. A.19.6 m
    2. B.29.4 m
    3. C.39.2 m
    4. D.73.5 m
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    Answer: B

21. Q372022 · 27 Jun 2022 · Shift 2
    
    1. A.$P_1>P_2$
    2. B.$P_1<P_2$
    3. C.$P_1=P_2$
    4. D.Insufficient data to draw any conclusion
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    Answer: A

22. Q562022 · 27 Jun 2022 · Shift 2· Numerical answer

    The current density in a cylindrical wire of radius $r=4.0\text{ mm}$ is $1.0\times 10^6{\text{ A/m}}^2$. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi \text{ A}$; where x is ________.

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    Answer: 12

23. Q532022 · 26 Jun 2022 · Shift 1· Numerical answer
    
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    Answer: 25

24. Q602022 · 26 Jun 2022 · Shift 1· Numerical answer
    
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    Answer: 363

25. Q362022 · 26 Jun 2022 · Shift 2

    If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number ${\mathrm{R}}_e$ is :

    1. A.${\mathrm{R}}_e=\frac{\eta d}{\rho v}$
    2. B.${\mathrm{R}}_e=\frac{\rho v}{\eta d}$
    3. C.${\mathrm{R}}_e=\frac{\rho vd}{\eta }$
    4. D.${\mathrm{R}}_e=\frac{\eta }{\rho vd}$
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    Answer: C