Properties of Solids & Fluids · JEE Main previous year questions

2020 13 questions

1. Q412020 · 6 Sept 2020 · Shift 1

   An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

   1. A.$f=\frac{1}{2\pi }\sqrt{\frac{YA}{mL}}$
   2. B.$f=\frac{1}{2\pi }\sqrt{\frac{mL}{YA}}$
   3. C.$f=\frac{1}{2\pi }\sqrt{\frac{YL}{mA}}$
   4. D.$f=\frac{1}{2\pi }\sqrt{\frac{mA}{YL}}$
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   Answer: A

2. Q362020 · 6 Sept 2020 · Shift 2

   A fluid is flowing through a horizontal pipe of varying cross-section, with speed $v\mathrm{m}{\mathrm{s}}^{-1}$ at a point where the pressure is P pascal. At another point where pressure is $\frac{P}{2}$ Pascal its speed is $V\mathrm{m}{\mathrm{s}}^{-1}$. If the density of the fluid is $\rho \mathrm{kg}{\mathrm{m}}^{-3}$ and the flow is streamline, then V is equal to :

   1. A.$\sqrt{\frac{P}{2\rho }+v^2}$
   2. B.$\sqrt{\frac{P}{\rho }+v^2}$
   3. C.$\sqrt{\frac{2P}{\rho }+v^2}$
   4. D.$\sqrt{\frac{P}{\rho }}+v$
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   Answer: B

3. Q342020 · 3 Sept 2020 · Shift 1

   Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

   1. A.4 : 1
   2. B.8 : 1
   3. C.2 : 1
   4. D.0.8 : 1
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   Answer: B

4. Q482020 · 3 Sept 2020 · Shift 1· Numerical answer

   When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to $0^{\circ }$, the surface tension of the liquid, in milliNewton $m-1$, is [${\rho }_{(\mathrm{liquid})}=900\mathrm{kg}{\mathrm{m}}^{-3}$, $g=10\mathrm{m}{\mathrm{s}}^{-2}$] (Give answer in closest integer) _______.

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   Answer: 101

5. Q432020 · 2 Sept 2020 · Shift 2

   A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05\mathrm{N}{\mathrm{m}}^{-1}$, density $=667\mathrm{kg}{\mathrm{m}}^{-3}$) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of $60^{\circ }$ with one another. Then h is close to ($g=10\mathrm{m}{\mathrm{s}}^{-2}$)

   1. A.0.049 m
   2. B.0.087 m
   3. C.0.137 m
   4. D.0.172 m
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   Answer: B

6. Q472020 · 2 Sept 2020 · Shift 2· Numerical answer

   A wire of density $9\times 10^{-3}\mathrm{kg}\mathrm{c}{\mathrm{m}}^{-3}$ is stretched between two clamps 1 m apart. The resulting strain in the wire is $4.9\times 10^{-4}$. The lowest frequency of the transverse vibrations in the wire is : (Young's modulus of wire $\mathrm{Y}=9\times 10^{10}\mathrm{N}{\mathrm{m}}^{-2}$), (to the nearest integer), _______.

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   Answer: 35

7. Q452020 · 9 Jan 2020 · Shift 1
   
   1. A.$1810{\text{ cm}}^3/\text{s}$
   2. B.$2420{\text{ cm}}^3/\text{s}$
   3. C.$3020{\text{ cm}}^3/\text{s}$
   4. D.$2720{\text{ cm}}^3/\text{s}$
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   Answer: D

8. Q492020 · 9 Jan 2020 · Shift 1· Numerical answer

   A body of mass $m=10\text{ kg}$ is attached to one end of a wire of length $0.3\text{ m}$. The maximum angular speed (in ${\text{rad s}}^{-1}$) with which it can be rotated about its other end in space station is : (Breaking stress of wire $=4.8\times 10^7{\text{ Nm}}^{-2}$ and area of cross-section of the wire $=10^{-2}{\text{ cm}}^2$) is:

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   Answer: 4

9. Q262020 · 9 Jan 2020 · Shift 2

   A wire of length L and mass per unit length $6.0\times 10^{-3}{\text{ kgm}}^{-1}$ is put under tension of 540 N. Two consecutive frequencies that it resonates at are : 420 Hz and 490 Hz. Then L in meters is :

   1. A.5.1 m
   2. B.2.1 m
   3. C.1.1 m
   4. D.8.1 m
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   Answer: B

10. Q322020 · 9 Jan 2020 · Shift 2

    A small spherical droplet of density d is floating exactly half immersed in a liquid of density $\rho$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

    1. A.$r=\sqrt{\frac{T}{(d-\rho )g}}$
    2. B.$r=\sqrt{\frac{2T}{3(d+\rho )g}}$
    3. C.$r=\sqrt{\frac{T}{(d+\rho )g}}$
    4. D.$r=\sqrt{\frac{3T}{(2d-\rho )g}}$
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    Answer: D

11. Q262020 · 8 Jan 2020 · Shift 1

    Consider a solid sphere of radius R and mass density $\rho (r)={\rho }_0\left(1-\frac{r^2}{R^2}\right),0<r\le R$ The minimum density of a liquid in which it will float is :

    1. A.$\frac{2{\rho }_0}{3}$
    2. B.$\frac{2{\rho }_0}{5}$
    3. C.$\frac{{\rho }_0}{5}$
    4. D.$\frac{{\rho }_0}{3}$
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    Answer: B

12. Q332020 · 7 Jan 2020 · Shift 1

    Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section $1.0{\text{ mm}}^2$) is $90{\text{ ms}}^{-1}$. If the Young's modulus of wire is $16\times 10^{11}{\text{ Nm}}^{-2}$, the extension of wire over its natural length is :

    1. A.0.03 mm
    2. B.0.04 mm
    3. C.0.02 mm
    4. D.0.01 mm
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    Answer: A

13. Q372020 · 7 Jan 2020 · Shift 2

    An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

    1. A.$\frac{3}{4}$
    2. B.$\frac{9}{16}$
    3. C.$\frac{\sqrt{3}}{2}$
    4. D.$\frac{81}{256}$
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    Answer: B