# Solved papers for JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन JEE PYQ-Fluid Mechanics, Surface Tension and Viscosity

### done JEE PYQ-Fluid Mechanics, Surface Tension and Viscosity Total Questions - 67

• question_answer1) A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in $m{{s}^{-1}}$) through a small hole on the side wall of the cylinder near its bottom, is                                                         [AIEEE 2002]

A)
10

B)
20

C)
$25.5$

D)
5

• question_answer2) Spherical balls of radius R are falling g in a viscous fluid of viscosity. The retarding viscous force acting on the spherical ball is                                                                                                            [AIEEE 2004]

A)
directly proportional to R but inversely proportional to v

B)
directly proportional to both radius R and velocity v

C)
Inversely proportional to both radius R and velocity v.

D)
Inversely proportional to R but directly proportional to velocity v.

• question_answer3) If two soap bubbles of different radii are connected by a tube                       [AIEEE 2004]

A)
air flows the bigger bubble to the smaller bubble till the sizes become equal

B)
air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C)
air flows from the smaller bubble to the bigger

D)
there is no flow of air

• question_answer4) A 20 cm long capillary tube is dipped, in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be                                      [AIEEE 2005]

A)
8cm

B)
10cm

C)
4cm

D)
20cm

• question_answer5) If the terminal speed of a sphere of gold (density$=19.5\text{ }kg/{{m}^{3}}$) is 0.2 m/s in a viscous liquid (density$=1.5\text{ }kg/{{m}^{3}}$), find the terminal speed of a sphere of silver (density =10.5$kg/{{m}^{3}}$) of the same size in the same liquid.                                                                                             [AIEEE 2006]

A)
0.4 m/s

B)
0.133 m/s

C)
0.1 m/s

D)
0.2 m/s

• question_answer6) A capillary tube is dipped in water. Another identical tube is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?                                             [AIEEE 2008]

A)

B)

C)

D)

• question_answer7) A jar is filled with two non-mixing liquids 1 and 2 having densities ${{\rho }_{1}}$ and ${{\rho }_{2}}$, respectively. A solid ball, made of a material of density ${{\rho }_{3}}$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${{\rho }_{1}},{{\rho }_{2}}$ and${{\rho }_{3}}$?                                                                                                                              [AIEEE 2008]

A)
${{\rho }_{1}}<{{\rho }_{2}}<{{\rho }_{3}}$

B)
${{\rho }_{1}}<{{\rho }_{3}}<{{\rho }_{2}}$

C)
${{\rho }_{3}}<{{\rho }_{1}}<{{\rho }_{2}}$

D)
${{\rho }_{1}}>{{\rho }_{3}}>{{\rho }_{2}}$

• question_answer8) A spherical solid ball of volume V is made of a material of density ${{\rho }_{1}}$. It is falling through a liquid of density ${{\rho }_{2}}\left( {{\rho }_{2}}<{{\rho }_{1}} \right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e.${{F}_{viscous}}=-k{{v}^{2}}(k>0)$. The terminal speed of the ball is                                                                                                                                      [AIEEE 2008]

A)
$\sqrt{\frac{Vg{{\rho }_{1}}}{k}}$

B)
$\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}$

C)
$\sqrt{\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}}$

D)
$\frac{Vg{{\rho}_{1}}}{k}$

• question_answer9) A ball is made of a material of density $\rho$ where ${{\rho }_{oil}}<\rho <{{\rho }_{water}}$ with ${{\rho }_{oil}}$ and ${{\rho }_{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position? [AIEEE 2010]

A)

B)

C)

D)

• question_answer10) Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution$=0.03\,\,N{{m}^{-1}}$)                                                                                  [AIEEE 2011]

A)
$0.4\,\,\pi$ m J

B)
$4\,\,\pi$ m J

C)
$0.2\,\,\pi$ m J

D)
$2\,\,\pi$ m J

• question_answer11) Water is flowing continuously from a tap having an internal diameter $8\times {{10}^{-3}}m$. The water velocity as it leaves the tap is $0.4\,m{{s}^{-1}}$. The diameter of the water stream at a distance $2\times {{10}^{-1}}m$ below the tap is close to                                                                                                  [AIEEE 2011]

A)
$3.6\times {{10}^{-3}}m$

B)
$5.0\times {{10}^{-3}}m$

C)
$7.5\times {{10}^{-3}}m$

D)
$9.6\times {{10}^{-3}}m$

• question_answer12) A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $\upsilon$, the total area around the fountain that gets wet is                                                                                 [AIEEE 2011]

A)
$\pi \frac{{{\upsilon }^{2}}}{{{g}^{2}}}$

B)
$\pi \frac{{{\upsilon }^{2}}}{g}$

C)
$\pi \frac{{{\upsilon }^{4}}}{{{g}^{2}}}$

D)
$\frac{\pi }{2}\frac{{{\upsilon }^{4}}}{{{g}^{2}}}$

• question_answer13) Two mercury drops (each of radius' r') merge to from bigger drop. The surface energy of the bigger drop, if T is the surface tension, is:                                                                                                          [AIEEE 11-05-2011]

A)
$4\eta {{r}^{2}}T$

B)
$2\eta {{r}^{2}}T$

C)
${{2}^{8/3}}\eta {{r}^{2}}T$

D)
${{2}^{5/3}}\eta {{r}^{2}}T$

• question_answer14)             If a ball of steel (density$p=7.8\text{ }gc{{m}^{-3}}$) attains a terminal velocity of $10cm\,{{s}^{-1}}$when falling in a water (Coefficient of Viscosity ${{\eta }_{water}}=8.5\times {{10}^{-4}}Pa.s$) then its terminal velocity in glycerine $(p=1.2gc{{m}^{-3}},\eta =13.2Pa.s.)$ would be, nearly:                                               [AIEEE 11-05-2011]

A)
$6.25\times {{10}^{-4}}cm\,{{s}^{-1}}$

B)
$6.45\times {{10}^{-4}}cm\,{{s}^{-1}}$

C)
$1.5\times {{10}^{-5}}cm\,{{s}^{-1}}$

D)
$1.6\times {{10}^{-5}}cm\,{{s}^{-1}}$

• question_answer15)  A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5\times {{10}^{-2}}$ N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is: [AIEEE 2012]

A)
0.0125 $N{{m}^{-1}}$

B)
0.1 $N{{m}^{-1}}$

C)
0.05 $N{{m}^{-1}}$

D)
0.025 $N{{m}^{-1}}$

• question_answer16)  A square hole of side length i is made at a depth of h and a circular hole of radius r is made at a depth of 4h from the surface of water in a water tank kept on a horizontal surface. If $\ell < A) \[\frac{\ell }{\sqrt{2\pi }}$

B)
$\frac{\ell }{\sqrt{3\pi }}$

C)
$\frac{\ell }{3\pi }$

D)
$\frac{\ell }{2\pi }$

• question_answer17) Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A' such that the ratio A/A' is 5. If the pressure difference of water between the two ends is $3\times {{10}^{5}}N{{m}^{-2}},$ the velocity of water with which it enters the tube will be (neglect gravity effects)                                [JEE ONLINE 12-05-2012]

A)
$5\,m\,{{s}^{-1}}$

B)
$10\,m\,{{s}^{-1}}$

C)
$25\,m\,{{s}^{-1}}$

D)
$50\sqrt{10}\,m\,{{s}^{-1}}$

• question_answer18) A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An Engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is (T = surface tension, $\rho$ = density)                                                                      [JEE ONLINE 19-05-2012]

A)
${{\left[ \frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}$

B)
${{\left[ \frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}$

C)
${{\left[ \frac{3T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}$

D)
${{\left[ \frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}$

• question_answer19) The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to [JEE ONLINE 26-05-2012]

A)
${{a}^{2}}$

B)
${{a}^{3}}$

C)
a

D)
${{a}^{-1}}$

• question_answer20)  In a cylindrical water tank, there are two small holes A and B on the wall at a depth of ${{h}_{1}},$ from the surface of water and at a height of ${{h}_{2}}$ from the bottom of water tank. Surface of water is at height of ${{h}_{2}}$ from the bottom of water tank. Surface of water is at height H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point & Find the ratio of ${{h}_{1}}$and ${{h}_{2}}$[JEE ONLINE 26-05-2012]

A)
Depends on H

B)
1 : 1

C)
2 : 2

D)
1 : 2

• question_answer21) A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged n a liquid  of density $\sigma$ at equilibrium position. The extension${{x}_{0}}$of the spring when it is in equilibrium is:                                             [JEE MAIN 2013]

A)
$\frac{Mg}{k}$

B)
$\frac{Mg}{k}\left( 1-\frac{LA\sigma }{M} \right)$

C)
$\frac{Mg}{k}\left( 1-\frac{LA\sigma }{2M} \right)$

D)
$\frac{Mg}{k}\left( 1+\frac{LA\sigma }{M} \right)$ (Here, k is spring constant)

• question_answer22) Assume that a drop of liquid evaporates by decrease in its surface energy. So that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is$\rho$and L is its latent heat of vaporization.                                                                                     [JEE MAIN 2013]

A)
$\frac{\rho L}{T}$

B)
$\sqrt{\frac{T}{\rho L}}$

C)
$\frac{T}{\rho L}$

D)
$\frac{2T}{\rho L}$

• question_answer23)  This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.                                                                     [JEE ONLINE 09-04-2013] Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height increases (if the density of the liquid and the angle of contact remain the same) Statement-2: Surface tension of a liquid decreases with the rise in its temperature.

A)
Statement -1 is true, Statement-2 is true. Statement-2 is not correct explanation for statement-1.

B)
Statement -1 is false. Statement -2 is true.

C)
Statement -1 is true. Statement-2 is false.

D)
[d] Statement-1 is true, Statement-2 is true. Statement-2 is correct explanation for statement-1.

• question_answer24) Air of density 1.2 $\operatorname{Kg}{{\operatorname{m}}^{-3}}$ is blowing across the horizontal wings of on aero plane in such a way that its speeds above and below the wings are $150\,\,m{{s}^{-1}}$ and $100\,\,m{{s}^{-1}}$, respectively. The pressure difference between the upper and lower                              [JEE ONLINE 22-04-2013]

A)
$60\operatorname{N}{{\operatorname{m}}^{-2}}$

B)
$180\operatorname{N}{{\operatorname{m}}^{-2}}$

C)
$7500\operatorname{N}{{\operatorname{m}}^{-2}}$

D)
$12500\operatorname{N}{{\operatorname{m}}^{-2}}$

• question_answer25) Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angel of contact $\theta$ and the height h up to which water rises change. These changes are:                                                                                                                                                [JEE ONLINE 23-04-2013]

A)
$\theta$increases and h also increases

B)
$\theta$ decreases and h also decreases

C)
$\theta$ increases and h decreases

D)
$\theta$ decreases and h increases

• question_answer26)   In an experiment, a small steel ball falls through a liquid at a constant speed of 10 cm/s. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward?            [JEE ONLINE 25-04-2013]

A)
5 cm/s

B)
Zero

C)
10 cm/s

D)
20 cm/s

• question_answer27) An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now?                                                                  [JEE MAIN 2014] (Atmospheric pressure = 76 cm of Hg)

A)
38 cm

B)
6 cm

C)
16 cm

D)
22 cm

• question_answer28)  There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${{d}_{1}}$ and ${{d}_{2}}$are filled in the tube. Each liquid subtends 90° angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{{{d}_{1}}}{{{d}_{2}}}$is [JEE MAIN 2014]

A)
$\frac{1+\tan \alpha }{1-\tan \alpha }$

B)
$\frac{1+\sin \alpha }{1-\cos \alpha }$

C)
$\frac{1+\sin \alpha }{1-\sin \alpha }$

D)
$\frac{1+\cos \alpha }{1-\cos \alpha }$

• question_answer29)  On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is : (density of water is ${{\rho }_{w}}$)  [JEE MAIN 2014]

A)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{T}}$

B)
${{R}^{2}}\sqrt{\frac{3{{\rho }_{w}}g}{T}}$

C)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{3T}}$

D)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{6T}}$

• question_answer30) Water is flowing at a speed of 1.5 $\text{m}{{\text{s}}^{\text{-1}}}$ through a horizontal tube of cross-sectional area $\text{1}{{\text{0}}^{\text{-2}}}{{\text{m}}^{\text{2}}}$and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water $\text{=1}{{\text{0}}^{3}}\text{kg}{{\text{m}}^{-3}}$)                               [JEE ONLINE 09-04-2014]

A)
15 N

B)
22.5 N

C)
33.7 N

D)
45 N

• question_answer31) A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio$\frac{x}{y}$is:                                [JEE ONLINE 09-04-2014]

A)
$\left( 1-\frac{d}{R} \right)$

B)
$\left( 1-\frac{2d}{R} \right)$

C)
$\left( \frac{R-d}{R+d} \right)$

D)
$\left( \frac{R+d}{R-d} \right)$

• question_answer32) The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of ${{10}^{9}}N{{m}^{-2}}.$For a given value of pressure, the fractional compression in volume is $\frac{\Delta V}{V}.$Which of the following statements about $\frac{\Delta V}{V}$for these three liquids is correct?                                                                                                                                            [JEE ONLINE 11-04-2014]

A)
Ethanol > Water > Mercury

B)
Water > Ethanol > Mercury

C)
Mercury > Ethanol > Water

D)
Ethanol > Mercury > Water

• question_answer33) A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 $m{{s}^{2}}$and density of water $={{10}^{3}}kg\,{{m}^{-3}}$)                 [JEE ONLINE 11-04-2014]

A)
$10.7m{{s}^{-1}}$

B)
$9.6m{{s}^{-1}}$

C)
$8.5m{{s}^{-1}}$

D)
$7.6m{{s}^{-1}}$

• question_answer34) An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density ${{10}^{3}}kg/{{m}^{3}}.$ The pressure inside the bubble is $1100N{{m}^{-2}}$ greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? $(g=9.8m{{s}^{-2}})$                                 [JEE ONLINE 11-04-2014]

A)
0.1m

B)
0.15m

C)
0.20m

D)
0.25m

• question_answer35) A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius a. The time in which it will be emptied is:                                                                      [JEE ONLINE 12-04-2014]

A)
$\frac{2A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}$

B)
$\frac{\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}$

C)
$\frac{2\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}$

D)
$\frac{A}{\sqrt{2}\pi {{a}^{2}}}\sqrt{\frac{h}{g}}$

• question_answer36) Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct?                                                                                                         [JEE ONLINE 12-04-2014]

A)
4PV + 3ST = 0

B)
3PV + 4ST = 0

C)
2PV + 3ST = 0

D)
3PV + 2ST = 0

• question_answer37) The velocity of water in a river is 18 km/h near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $={{10}^{-2}}$ poise.       [JEE ONLINE 19-04-2014]

A)
${{10}^{-1}}N/{{m}^{2}}$

B)
${{10}^{-2}}N/{{m}^{2}}$

C)
${{10}^{-3}}N/{{m}^{2}}$

D)
${{10}^{-4}}N/{{m}^{2}}$

• question_answer38)  In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of the tube at A and B is $6m{{m}^{2}}$and $10m{{m}^{2}}$10 mm2 respectively. The rate at which water flows through the tube is $(g=10\,m{{s}^{-2}})$ [JEE ONLINE 19-04-2014]

A)
7.5 cc/s

B)
8.0 cc/s

C)
10.0 cc/s

D)
12.5 cc/s

• question_answer39) A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T, density $\rho$)                                                                         [JEE ONLINE 19-04-2014]

A)
$\sqrt{\frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

B)
$\sqrt{\frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

C)
$\sqrt{\frac{4T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

D)
$\sqrt{\frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right)}$

• question_answer40) If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter$\frac{2}{\sqrt{\pi }}cm$then the Reynolds number for the flow is (density of water $={{10}^{3}}kg/{{m}^{3}}$and viscosity of water $={{10}^{-3}}Pa.s$) close to:                 [JEE ONLINE 10-04-2015]

A)
11,000

B)
5500

C)
550

D)
1100

• question_answer41)  If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by:     [JEE ONLINE 10-04-2015]

A)
$\frac{4T}{R}$

B)
$\frac{2T}{R}$

C)
$\frac{T}{2R}$

D)
None of these

• question_answer42) A beaker contains a fluid of density$\rho \,kg/{{m}^{3}},$ specific heat $S\text{ }J/kg{}^\circ C$and viscosity t| . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $(\overset{\bullet }{\mathop{Q}}\,/A)$by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta ,\left( \frac{S\Delta \theta }{h} \right)$and$\left( \frac{1}{\rho g} \right)$when $\Delta \theta$ (in °C) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(\overset{\bullet }{\mathop{Q}}\,/A)$is:                                                                                                                       [JEE MAIN 11-04-2015]

A)
$\eta \frac{S\Delta \theta }{h}$

B)

•  $\eta \left( \frac{S\Delta \theta }{h} \right)\left( \frac{1}{\rho g} \right)$

C)
$\frac{S\Delta \theta }{\eta h}$

D)

$\left( \frac{S\Delta \theta }{\eta h} \right)\left( \frac{1}{\rho g} \right)$

• Which of the following option correctly describes the variation of the speed v and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F = -kv, where 'k' is constant, on the body? (Graphs are schematic and not drawn to scale)                                                                            [JEE ONLINE 09-04-2016]

A)

B)

C)

D)

• question_answer44)  Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r < < R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then:      [JEE ONLINE 09-04-2016]

A)
$x=r{{\left( \frac{H}{H+h} \right)}^{2}}$

B)
$x=r\left( \frac{H}{H+h} \right)$

C)
$x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{4}}}$

D)

$x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{2}}}$

• question_answer45)  The following observations were taken for determining surface tensiton T of water by capillary method : Diameter of capilary, $D=1.25\times {{10}^{-2}}m$ rise of water, $h=1.45\times {{10}^{-2}}m$ Using $g=9.80\,m/{{s}^{2}}$and the simplified relation$\text{T=}\frac{\text{rhg}}{\text{2}}\text{ }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\,\text{N/m,}$ the possible error in surface tension is closest to:     [JEE Main 2017]

A)
2.4%

B)
10%

C)
0.15%

D)
1.5%

• question_answer46) Two tubes of radii ${{r}_{1}}$ and ${{r}_{2}},$ and lengths ${{I}_{1}}$ and ${{I}_{2}},$ respectively, are connected in series and a liquid flows through each of them in stream line conditions. ${{P}_{1}}$ and ${{P}_{2}}$ are pressure differences across the two tubes. If ${{P}_{2}}$ is $4{{P}_{1}}$ and ${{I}_{2}}$ is $\frac{{{I}_{1}}}{4},$ then the radius ${{r}_{2}}$ will be equal to -                                                                             [JEE Online 09-04-2017]

A)
$4{{r}_{1}}$

B)
${{r}_{1}}$

C)
$2{{r}_{1}}$

D)
$\frac{{{r}_{1}}}{2}$

• question_answer47) A thin uniform tube is bent into a circle of radius in the vertical plane. Equal volumes of two immiscible liquids, whose densities are and fill half the circle. The angle between the radius vector passing through the common interface and the vertical is:                                                                                               [JEE Online 15-04-2018]

A)
$\theta ={{\tan }^{-1}}\left[ \frac{\pi }{2}\left( \frac{{{\rho }_{1}}-{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}} \right) \right]$

B)
$\theta ={{\tan }^{-1}}\frac{\pi }{2}\left( \frac{{{\rho }_{1}}-{{\rho }_{2}}}{{{\rho }_{1}}+{{\rho }_{2}}} \right)$

C)
$\theta ={{\tan }^{-1}}\pi \left( \frac{{{\rho }_{1}}}{{{\rho }_{2}}} \right)$

D)
None of above

• question_answer48) When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes$\frac{5r}{4}$. Taking the atmospheric pressure to be equal to $10m$ height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):                                            [JEE Online 15-04-2018 (II)]

A)
$10.5m$

B)
$8.7m$

C)
$11.2m$

D)
$9.5m$

• question_answer49) A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let ${{P}_{2}}$be the pressure inside the inner bubble and${{P}_{0}},$the pressure outside the outer bubble. Radius of another bubble with pressure difference ${{P}_{2}}-{{P}_{0}}$ between its inside and outside would be                                                                                                                                     [JEE Main Online 16-4-2018]

A)
6 cm

B)
12 cm

C)
4.8 cm

D)
2.4 cm

• question_answer50) A surface of certain metal is first illuminated with light of wavelength ${{\lambda}_{1}}=350\,nm$ nm and then, by light of wavelength ${{\lambda }_{2}}=540nm$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to: (Energy of photon $=\frac{1240}{\lambda \,(in\,\,nm)}\,e\,V)$                                                                                    [JEE Main 09-Jan-2019 Morning]

A)
5.6

B)
2.5

C)
1.8

D)
1.4

• question_answer51) The top of a water tank is open to air and its water level maintained. It is giving out $0.74\text{ }{{m}^{3}}$ water per minute through a circular opening of 2 cm radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to:                                                             [JEE Main 09-Jan-2019 Evening]

A)
6.0 m

B)
9.6 m

C)
2.9 m

D)
4.8 m

• question_answer52) Water flows into a large tank with flat bottom at the rate of${{10}^{-}}^{4}{{m}^{3}}{{s}^{-1}}$. Water is also leaking out of a hole of area $1\,c{{m}^{2}}$ at its bottom. If the height of the water in the tank remains steady, then this height is- [JEE Main 10-Jan-2019 Morning]

A)
2.9 cm

B)
5.1 cm

C)
4 cm

D)
1.7 cm

• question_answer53) A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by- [JEE Main 12-Jan-2019 Evening]

A)

B)

C)

D)
None of these

• question_answer54) Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water $=1000kg/{{m}^{3}},$coefficient of viscosity of water = 1mPas) [JEE Main 8-4-2019 Morning]

A)
${{10}^{6}}$

B)
${{10}^{3}}$

C)
${{10}^{4}}$

D)
${{10}^{2}}$

• question_answer55) If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-               [JEE Main 8-4-2019 Afternoon]

A)
${{S}^{3/2}}{{I}^{1/2}}{{h}^{0}}$

B)
${{S}^{1/2}}{{I}^{1/2}}{{h}^{0}}$

C)
${{S}^{1/2}}{{I}^{1/2}}{{h}^{-1}}$

D)
${{S}^{1/2}}{{I}^{3/2}}{{h}^{-1}}$

• question_answer56) If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :                                                                           [JEE Main 9-4-2019 Morning]

A)
$4M$

B)
$M$

C)
$2M$

D)
$\frac{M}{2}$

• question_answer57) A wooden block floating in a bucket of water has$\frac{4}{5}$of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:                                         [JEE Main 9-4-2019 Afternoon]

A)
0.5

B)
0.7

C)
0.6

D)
0.8

• question_answer58) The radtio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to$135{}^\circ$and$0{}^\circ ,$respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius ${{r}_{1}},$ while water rises by the same amount h in a capillary tube of radius ${{r}_{2}}.$The ratio, $({{r}_{1}}/{{r}_{2}}),$is then close to:                          [JEE Main 10-4-2019 Morning]

A)
2/3

B)
3/5

C)
2/5

D)
4/5

• question_answer59) A submarine experiences a pressure of $5.05\times {{10}^{6}}$Pa at a depth of ${{d}_{1}}$in a sea. When it goes further to a depth of ${{d}_{2}},$it experiences a pressure of $8.08\times {{10}^{6}}Pa.,$Then${{d}_{2}}-{{d}_{1}}$is approximately (density of water $={{10}^{3}}kg/{{m}^{3}}$and acceleration due to gravity $=10m{{s}^{-2}}$)                                                                        [JEE Main 10-4-2019 Afternoon]

A)
500 m

B)
400 m

C)
300 m

D)
600 m

• question_answer60) Water from a tap emerges vertically downwards with an initial speed of $1.0m{{s}^{-1}}.$The cross-sectional area of the tap is ${{10}^{-4}}{{m}^{2}}.$ Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be: (Take $g=10m{{s}^{-2}}$) [JEE Main 10-4-2019 Afternoon]

A)
s  $1\times {{10}^{5}}{{m}^{2}}$

B)
$5\times {{10}^{5}}{{m}^{2}}$

C)
$2\times {{10}^{5}}{{m}^{2}}$

D)
$5\times {{10}^{4}}{{m}^{2}}$

• question_answer61) A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? (Take density of water $={{10}^{3}}kg/{{m}^{3}}$) [JEE Main 10-4-2019 Afternoon]

A)
65.4 kg

B)
87.5 kg

C)
30.1 kg

D)
46.3 kg

• question_answer62) A solid sphere, of radius R acquires a terminal velocity${{\text{v}}_{1}}$when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, ${{\text{v}}_{2}},$when falling through the same fluid, the ratio $\text{(}{{\text{v}}_{1}}/{{\text{v}}_{2}})$equals :      [JEE Main 12-4-2019 Afternoon]

A)
1/27

B)
1/9

C)
27

D)
9

• question_answer63) 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:      [JEE MAIN Held on 07-01-2020 Evening]

A)
$\frac{81}{256}$

B)
$\frac{9}{16}$

C)
$\frac{3}{4}$

D)
$\frac{\sqrt{3}}{2}$

• question_answer64) 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: [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{2{{\rho }_{0}}}{5}$

B)
$\frac{{{\rho }_{0}}}{3}$

C)
$\frac{{{\rho }_{0}}}{5}$

D)
$\frac{2{{\rho }_{0}}}{3}$

• question_answer65) A leak proof cylinder of length 1 m, made of a Metal which has very low coefficient of expansion is floating vertically in water at $0{}^\circ C$such that its height above the water surface is 20 cm. When the temperature of water is increased to $4{}^\circ C,$ the height of the cylinder above the water surface becomes 21 cm. The density of water at $T=4{}^\circ C,$relative to the density at $T=0{}^\circ C$is close to [JEE MAIN Held On 08-01-2020 Morning]

A)
1.04

B)
1.03

C)
1.26

D)

1.01

• question_answer66)  Water flows in a horizontal tube (see figure). The pressure of water changes by 700 $N{{m}^{2}}$ between A and B where the area of cross section are 40 $c{{m}^{2}}$and 20$c{{m}^{2}}$, respectively. Find the rate of flow of water through the tube. (density of water = 1000$kg{{m}^{3}}$)
[JEE MAIN Held on 09-01-2020 Morning]

A)
$3020c{{m}^{3}}/s$

B)
$1810c{{m}^{3}}/s$

C)
$2720c{{m}^{3}}/s$

D)
$2420c{{m}^{3}}/s$

• question_answer67) 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) [JEE MAIN Held on 09-01-2020 Evening]

A)
$r=\sqrt{\frac{3T}{(2d-\rho )g}}$

B)
$r=\sqrt{\frac{T}{(d+\rho )g}}$

C)
$r=\sqrt{\frac{T}{(d-\rho )g}}$

D)
$r=\sqrt{\frac{2T}{3(d+\rho )g}}$