Properties of Solids & Fluids · JEE Main previous year questions

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 ________ $\times 10^{-5}$

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 ($n_w=4/3$) ________.

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

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 $\pi =\frac{22}{7}$ )

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.$2.26\times 10^{-5}\text{ J}$

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 ________.

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.$9.68\times 10^{-4}\text{ J}$

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.$1:10$

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.$0.10$

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.$\sigma =\frac{6K-2\eta }{3K-2\eta }$

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.$\frac{3}{T}$

Surface tension of a soap bubble is $2.0\times 10^{-2}\mathrm{N}{\mathrm{m}}^{-1}$. Work done to increase the radius of soap bubble from $3.5\mathrm{cm}$ to $7\mathrm{cm}$ will be: Take $\left[\pi =\frac{22}{7}\right]$

1. A.$18.48\times 10^{-4}\mathrm{J}$
2. B.$5.76\times 10^{-4}\mathrm{J}$
3. C.$0.72\times 10^{-4}\mathrm{J}$
4. D.$9.24\times 10^{-4}\mathrm{J}$

A bicycle tyre is filled with air having pressure of $270\mathrm{kPa}$ at $27^{\circ }\mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ }\mathrm{C}$ is

1. A.262 kPa
2. B.360 kPa
3. C.270 kPa
4. D.278 kPa

Match List I with List II $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{A.}& \text{Surface tension}& \text{I.}& \mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}\\ \text{B.}& \text{Pressure}& \text{II.}& \mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}\\ \text{C.}& \text{Viscosity}& \text{III.}& \mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-2}\\ \text{D.}& \text{Impulse}& \text{IV.}& \mathrm{kg}{\mathrm{s}}^{-2}\end{array}$$ Choose the correct answer from the options given below :

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

Match List I with List II $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{A.}& \text{Young’s Modulus (Y)}& \text{I.}& [\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}]\\ \text{B.}& \text{Co-efficient of Viscosity }(\eta )& \text{II.}& [\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}]\\ \text{C.}& \text{Planck’s Constant (h)}& \text{III.}& [\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}]\\ \text{D.}& \text{Work function }(\phi )& \text{IV.}& [\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}]\end{array}$$ Choose the correct answer from the options given below :

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

A $100\mathrm{m}$ long wire having cross-sectional area $6.25\times 10^{-4}{\mathrm{m}}^2$ and Young's modulus is $10^{10}\mathrm{N}{\mathrm{m}}^{-2}$ is subjected to a load of $250\mathrm{N}$, then the elongation in the wire will be :

1. A.$6.25\times 10^{-6}\mathrm{m}$
2. B.$4\times 10^{-3}\mathrm{m}$
3. C.$4\times 10^{-4}\mathrm{m}$
4. D.$6.25\times 10^{-3}\mathrm{m}$

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

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

The frequency $(\nu )$ of an oscillating liquid drop may depend upon radius $(r)$ of the drop, density $(\rho )$ of liquid and the surface tension (s) of the liquid as $\nu =r^a{\rho }^b{s}^c$. The values of a, b and c respectively are

1. A.$\left(\frac{3}{2},\frac{1}{2},-\frac{1}{2}\right)$
2. B.$\left(-\frac{3}{2},-\frac{1}{2},\frac{1}{2}\right)$
3. C.$\left(\frac{3}{2},-\frac{1}{2},\frac{1}{2}\right)$
4. D.$\left(-\frac{3}{2},\frac{1}{2},\frac{1}{2}\right)$

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $3696\times 10^{-x}\mathrm{N}$. The value of $x$ is _______. (Given, $\mathrm{g}=9.8m/{\mathrm{s}}^2$ and $\pi =\frac{22}{7}$)

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

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 ____ $\mathrm{m}{\mathrm{s}}^{-1}$.

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.$2.5\times 10^7\text{ N}$

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).

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.$400\text{ N}$