Properties of Solids & Fluids · JEE Main previous year questions

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

1. A.$(P_1-P_2{)}^2$
2. B.$\sqrt{P_1-P_2}$
3. C.$P_1-P_2$
4. D.$(P_1-P_2{)}^4$

An air bubble of radius $1.0\text{ mm}$ is observed at a depth $20\text{ cm}$ below the free surface of a liquid having surface tension $0.095{\text{ J/m}}^2$ and density $10^3{\text{ kg/m}}^3$. The difference between pressure inside the bubble and atmospheric pressure is _________ ${\text{N/m}}^2$. (Take $g=10{\text{ m/s}}^2$ )

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ${\rho }_1$ and ${\rho }_2$, respectively. The frequency of $9^{\text{th}}$ harmonic of closed tube is identical with $4^{\text{th}}$ harmonic of open tube. If the length of the closed tube is $10\text{ cm}$ and the density ratio of the gases is ${\rho }_1:{\rho }_2=1:16$, then the length of the open tube is :

1. A.$\frac{15}{7}\text{ cm}$
2. B.$\frac{20}{9}\text{ cm}$
3. C.$\frac{20}{7}\text{ cm}$
4. D.$\frac{15}{9}\text{ cm}$

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is _________.

A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is :

1. A.${\left(\frac{\sigma -2}{\sigma +2}\right)}^{1/3}$
2. B.${\left(\frac{\sigma +1}{\sigma -1}\right)}^{1/3}$
3. C.${\left(\frac{\sigma -1}{\sigma }\right)}^{1/3}$
4. D.${\left(\frac{\sigma }{\sigma -1}\right)}^{1/3}$

Two persons pull a wire towards themselves. Each person exerts a force of $200\text{ N}$ on the wire. Young's modulus of the material of wire is $1\times 10^{11}{\text{ N m}}^{-2}$. Original length of the wire is $2\text{ m}$ and the area of cross section is $2{\text{ cm}}^2$. The wire will extend in length by ______ $\mu \text{m}$.

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

1. A.$1:9$
2. B.$1:27$
3. C.$1:81$
4. D.$1:3$

A spherical ball of radius $1\times 10^{-4}\mathrm{m}$ and density $10^{5}kg/{\mathrm{m}}^3$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately: (The coefficient of viscosity of water is $9.8\times 10^{-6}\mathrm{N}s/{\mathrm{m}}^2$)

1. A.$2518\mathrm{m}$
2. B.$2396\mathrm{m}$
3. C.$2249\mathrm{m}$
4. D.$2296\mathrm{m}$

Correct Bernoulli's equation is (symbols have their usual meaning) :

1. A.$P+\frac{1}{2}\rho gh+\frac{1}{2}\rho v^2=\text{constant}$
2. B.$P+mgh+\frac{1}{2}m{v}^2=\text{constant}$
3. C.$P+\rho gh+\rho v^2=\text{constant}$
4. D.$P+\rho gh+\frac{1}{2}\rho v^2=\text{constant}$

A liquid column of height $0.04\text{ cm}$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $8\times 10^3{\text{ kg m}}^{-3}$ and surface tension of soap solution is $0.28{\text{ Nm}}^{-1}$, then diameter of the soap bubble is ________ $\text{cm}$. (if $g=10{\text{ m s}}^{-2}$ )

1. A.$5:4$
2. B.$9:10$
3. C.$8:9$
4. D.$1:1$

Small water droplets of radius $0.01\mathrm{mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10cm/s$. Due to condensation, if $8$ such droplets are coalesced and formed a larger drop, the new terminal velocity will be ____ $cm/s$.

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $\mathrm{R}=$ Radius of bubble, $\mathrm{S}=$ Surface tension of bubble)

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

Match List I with List II : $$\begin{array}{llll}& \text{LIST I}& & \text{LIST II}\\ \text{A.}& \text{A force that restores an elastic body of unit area to its original state}& \text{I.}& \text{Bulk modulus}\\ \text{B.}& \text{Two equal and opposite forces parallel to opposite faces}& \text{II.}& \text{Young’s modulus}\\ \text{C.}& \text{Forces perpendicular everywhere to the surface per unit area same everywhere}& \text{III.}& \text{Stress}\\ \text{D.}& \text{Two equal and opposite forces perpendicular to opposite faces}& \text{IV.}& \text{Shear modulus}\end{array}$$ Choose the correct answer from the options given below :

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

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

1. A.To protect tyres from catching dirt from ground
2. B.It is a custom
3. C.To alert other vehicles
4. D.To conduct excess charge due to air friction to ground and prevent sparking

A sonometer wire of resonating length $90\mathrm{cm}$ has a fundamental frequency of $400\mathrm{Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600\mathrm{Hz}$ under same tension ____ $\mathrm{cm}$.

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

A soap bubble is blown to a diameter of $7\mathrm{cm}$. $36960\mathrm{erg}$ of work is done in blowing it further. If surface tension of soap solution is $40dyne/cm$ then the new radius is ____ $\mathrm{cm}$. Take $\left(\pi =\frac{22}{7}\right)$.

Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. 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.Both Statement I and Statement II are true.
3. C.Statement I is false but Statement II is true.
4. D.Statement I is true but Statement II is false.

Mercury is filled in a tube of radius $2\text{ cm}$ up to a height of $30\text{ cm}$. The force exerted by mercury on the bottom of the tube is ________ $\text{N}$. (Given, atmospheric pressure $=10^5\text{ N}{\text{m}}^{-2}$, density of mercury $=1.36\times 10^4{\text{ kg m}}^{-3}$, $g=10\text{ m}{\text{s}}^{-2}$, $\pi =\frac{22}{7}$)

With rise in temperature, the Young's modulus of elasticity :

1. A.changes erratically
2. B.increases
3. C.decreases
4. D.remains unchanged

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\text{ km/s}$, the root mean square velocity of oxygen at the same condition in $\text{km/s}$ is :

1. A.1.0
2. B.1.5
3. C.2.0
4. D.0.5

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02\%$ is ____ $m$. (Take density of sea water $=10^3\mathrm{kg}{\mathrm{m}}^{-3}$, Bulk modulus of rubber $=9\times 10^8\mathrm{N}{\mathrm{m}}^{-2}$, and $g=10\mathrm{m}{\mathrm{s}}^{-2}$)