Fluids Questions and Answers

A small spherical ball of density 5p is released from rest in a vessel filled with liquid of density p Vessel is given acceleration of 10 m s If to is time taken by ball to hit the wall of vessel and ao be the acceleration of ball then 2 m s i A ao a C to 2s 4m FO 16 m B 20 B a 2 m s D to 1s

On dipping a capillary of radius r in water water rises upto a height H and potential energy of water is u If a capillary of radius 2r is dipped in water U then the potential energy is u The ratio 42 1 2 1 2 3 4 1 is U2 4 1 1

19 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 3 Jo 2 334 3 81 256 16

Assuming the bulk modulus B is constant for sea water we can derive an expression for the density variation with depth h below the surface Show that the result may be written p p bh where p is the density at the surface y de tu B 1 zv for fun Evaluate the constant b A Pag B B Pog B C 2pog B Ted Radfah D Pog 2B

A ball is made of a material of density p where p P P with P and Prepresenting 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 1 Kader water 3 wake

If a ball of steel density p 7 8 g cm attains a terminal velocity of 10 cm s when falling in a tank of water coefficient of viscosity 8 5x 10 Pa s then its terminal velocity in glycerine p 1 2 g cm 13 2 Pa s would be nearly AIEEE 2011 1 1 6 x 10 cm s 3 6 45 x 10 cm s 2 6 25 x 10 cm s 4 1 5 x 10 cm s

An open tank of height 3 m and square base of area 25 m containing water up to a height of 2 m is accelerated horizontally Maximum acceleration of container such that water does not spill is 1 4 m s 3 1 m s2 2 2 m s 4 8 m s2

From a water tap liquid comes out in form of cylinder As water moves down radius of that cylinder decreases Consider a very small element of height h and radius R due to small height radius is assumed to be constant Ch This element is given in the diagram An imaginary cross section ABCD divides this element in two equal semi cylinders S is surface tension of liquid Now choose correct statement s B D A Surface energy of this elementary cylinder is S 27Rh 2 R 2S B Pressure inside the cylinder is more than atmospheric pressure by R C Force exerted by one half cylinder on another half cylinder due to surface tension is 2Sh

An empty bowl is floating on the tub filled with water The wall thickness of the bowl is very low so the weight and volume of the material in the bowl can be ignored A If one pushes the bowl it goes down How much force would be required to hold the bowl completely submerged just below the water surface as shown in the second image Force equal to the weight of water the bowl can contain

30 Two spherical soap bubble coalesce If y be the change in volume of th contained air A is the change in total surface area then show that 3PV 4A 0 where T is the surface tension and P is atmospheric pressure

Between two parallel long wires AB and CD is a soap film S between another two transverse wires PQ EF The separation between PQ EF is x which can be varied The correct statement s is are Force due to surface tension on PQ equals in magnitude to that on EF Force of surface tension on PQ is proportional to the separation x Force of surface tension on PQ is proportional to length of PQ Surface energy depends on x P JB

neet prep Mechanical Properties of Fluids 1 remain at the same height 2 fall at the rate of 1 cm h 3 fall at the rate of 2 cm h 4 go up at the rate of 1 cm h in a cylindrical container of diameter D D d as shown in figure It is burning at the rate f 2 cm hour then the top of the candle will Contact Number 9667591930 852752171 and from to zero is 1 2 2 3 2 1 4 11 A clock with a metal pendulum beating seconds keep correct time at 0 C If it loses 12 5 s a day at 25 C the coefficient of linear expansion of metal pendulum is 1 2 3 86400 43200 E C 14400 C

para tong wes AB and CD is a soap tim 5 between another two transverse wres PQ EF The separation between PQ EF is x which can be varied FD

A thin liquid film formed between a U shaped wire and a light slider supports a weight 15 x 10 N see figure The length of the slider is 30 cm and its weight negligible The surfar tension of the liquid film is AIEEE 2012

The top of a water tank is open to air and its water level is maintained It is giving out 0 74 m wate per minute through a circular opening of 2 cm radius in its wall The depth of the centre of the opening from the level of water in the tank is close to LJEE Main 2019 Jan 1 9 6 m 2 4 8 m 3 2 9 m 4 6 0 m

There is a hole of area A at the bottom of cylindrical vessel Water is filled up to a height hand water flows out in t second If water is filled to a height 4h it will flow out in time equal to Ot 4t 2t

22 A resonance tube is old and has jagged end It is still used in the laboratory to determine velocity of sound in air A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark near the open end of the tube The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark The velocity of sound in air obtained in the experiment is close to 1 322 ms 1 2 3 335 ms 1 341 ms 4 328 ms 1

An incompressible liquid travels as shown in fig 29 The speed of the fluid in the lower branch will be 0 12 m 1 1 ms 3 2 25 ms 0 3 ms 0 12 m 0 18 m 2 1 5 ms 4 3 ms 1 5 ms 36 37 ameftame 0 12 m 1 1 3 2

e 23 Three identical particles are joined together by a thread as shown All the three particles are moving in a horizontal plane If the velocity of the outermost particle is vo then the ratio of tensions in the three sections of the string is 0 O m L 21 1 3 5 6 3 6 9 9 10 m 3L 2 3 4 5 4 7 6

ution Ans stration 15 Which of the following conditions should be more favourable for increasing the rate of forwm reaction in the equilibrium H H H AH ve 1 2000 C temperature and 760 mm of Hg pressure 2 3500 C temperature and 100 cm of Hg pressure 3 3500 C temperature and 1 mm of Hg pressure 4 All are wrong

1 Fluid is flowing in a straight sanitary pipe of diameter 40 mm The liquid has a density of 1030 kg m and viscosity of 0 05 Pa s If the volumetric flow rate is 0 002 m s what is the maximum fluid velocity in the pipe 20pts

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends The tube is then rotates in a horizontal plane about one of its ends with a uniform angular velocity w The force exerted by the liquid at the other end is a Mw L 2 b Mw L c Mw L 4 d Mw L 2

A jet of water with cross section of 6 cm strikes a wall at ar angle of 60 to the normal and rebounds elastically from the wall without losing energy If the velocity of the water in the jet is 12 m s the force acting on the wall is 0 864 N 86 4 N 72 N O 7 2 N

In the figure shown a cone of density p and total height floats in a liquid of density p The height of the cone above the liquid is h If the mass of the cone is 38 kg and P 19 27 A P h 8 127 C The force acting on the curved surface of the cone is 160 N D The force acting on the base of the cone is 380 N then identify the correct statements B h 2

and pour A hollow spherical ball is half submerged in water Through one tap water is taken out and through another tap a liquid of density double the density of water is poured in tank such that volume of liquid in tank remains constant Sphere will a go down b go up 11

Consider the following statements and identify the correct answer 1 Surface tension of liquids generally decreases with rise in temperature II Viscosity of gases generally decreases with rise in temperature III Viscosity of liquids generally decreases with rise in temperature A I II are only true B II III are only true C I III are only true D All are true

A thin uniform cylindrical shell closed at both ends is partially filled with water It is floating vertically in water in half submerged state If pc is the relative density of the material of the shell with respect to water then the correct statement is that the shell is A more than half filled if pc is less than 0 5 B more than half filled if pc is more than 1 0 C half filled if p is more than 0 5 D less than half filled if p is less than 0 5

In a U tube as shown in figure water and oil a in the left side and right side of the tube respectivel The heights from the bottom for water and columns are 15 cm and 20 cm respectively Th density of the oil is take pwater 1000 kg m 15cm water 1 1200 kg m 3 1000 kg m 20cm oil 2 750 kg m 4 1333 kg m 3

3 20 min 4 15 min Two small spherical metal balls having equal masses are made from materials of densities p and P1 P2 P1 8p2 and have radii of 1mm and 2mm respectively They are made to fall vertically from rest in a viscous medium whose coefficient of viscosity equals n and whose density is 0 1 p2 The ratio of their terminal velocities would be 1 79 72 2 19 36 3 39 72 4 79 36

1 In a two litre metallic bottle air is pumped to a pressure of 2 0 atm A thin plastic bag of large capacity greater than 10 L with no air inside is connected to the opening of the bottle that is closed Bottle together with the bag is placed on one pan of balance and weights are put on the other pan to establish balance When the opening of the bottle is opened air flows from the bottle into the bag and the balance may be disturbed How much additional weight is required to reestablish balance Density of air is 1 3 kg m and acceleration of free fall is 10 m s a 0 0 g c 1 3 g b 0 6 g 2 6 g

A long capillary tube of radius 0 2 mm is placed vertically inside a beaker of water Water rises to a hight of 7 05 cm in the tube making zero angle os contact Now if tube is pushed into water so that only 5 cm of its length is above the surface What is the new angle of contact in degrees between water and glass surface Take 2 1 41 surface tension of water 0 07 N m

The velocity of efflux from a small hole made at bottom of a container as a function of height y of water in tank is Straight line Parabola Ellipse

Consider fully developed laminar flow in a circular pipe shown below Use a cylindrical control volume CV as shown Indicate the forces acting on the control volume Using the momentum balance equation develop an expression for the velocity distribution L TE CV

a 3 12 27 A plank of area of cross section A is half immersed in liquid 1 of density p and half in liquid 2 of density 2p What is period of oscillation of the plank if it is slightly depressed downwards m VpAg 3m 2 pAg 8 A mass M is performing line a 2 2 c 2 b T P d 2 2p m VpAg m 3 pAg

depth 10th below water surface The range of water issuing o of the hole is R on ground What extra pressure must be applied on the water surface so that the range become 2R take 1 atm 105 Pa and g 10 ms 155 A large tank is filled with water density 10 kgm 3 A small hole is made at a 3 10m R

A cylindrical container of the shape shown in the figure has a diameter of 0 9 m at the top and 0 3 m at the bottom A horizontal capillary tube of length L inner radius a and outer radius 0 002 m is fixed at the bottom of the container The container is filled with a liquid of density p 1 6 x 10 kg m to a height H above the tube and a pressure P is applied on the top The rate of flow of liquid from the tube is Q 8 x 10 7 m s With the same P and H and the tube removed the liquid comes out with a speed of v 10 m s Determine he viscosity n in Ns m2 of the liquid Given ta 2 x 10 6 m and a L 10 6 m 2003 20

uniform 156 A wooden water cross section is hinged at one end to the bottom of height of 0 5 m The specific gravity of the planki 0 5 The angle 0 made by the plank in equilibrium tank as shown The tank is filled with position is a 30 0 b 45 c 60 0 5m

A symmetrical right circular cone of wood floats in fresh water with axis vertical and the apex down The axial height of the cone is 1 unit The submerged portion has a height h measured upwards from the apex What would be the height of the centre of buoyancy from the apex a c 1 22 3 h b 58 314 h d h

A spherical ball of radius R is made by joining two hemispherical parts The two parts have density p and 2p When placed in a water tank the ball floats while remaining completely submerged Neglect viscous forces Mark the correct statement s 2p 3 A Density of water is p then p R B Position of centre of mass of ball is at distance of 123 160 C Moment of inertia of ball about COM of ball perpendicular to the plane of paper is D Time period of small angular oscillations of the ball about its equilibrium position is given by 2n 123R 40g 20 from O water R

In a streamline flow The speed of a particle always remains same The velocity of a particle always remains same The kinetic energies of all the particles arriving at a given points are not same The moments of all the particles arriving at a given points are same

11 On increasing temperature of a liquid its surface tension generally 1 Increases 2 Decreases 3 Remains constant 4 First increases and then decreases

A 90 N rectangular solid block slides down a 30 inclined plane The plane is lubricated by a 3 mm thick film of oil of relative density 0 90 and viscosity 8 0 poise If the contact area is 0 3 m estimate the terminal velocity of the block

A large cylindrical tank of cross sectional area 1m is filled with water It has a small hole at a height of I m from the bottom A movable piston of mass 5 kg is fitted on the top of the tank such that it can slide in the tank freely A load of 45 kg is applied on the top of water by piston as shown in figure Find the value of v when piston is 7m above the bottom g 10 m s

As the drawing illustrates a pond full of water has the shape of an inverted cone with the tip sliced off and has a depth of 30m The atmospheric pressure above the pond is 1 0 x10 Pa The circular top surface radius R and circular bottom surface radius R of the pond are both parallel to the ground The magnitude of the force acting on the top surface by the liquid is the same as the magnitude R of the force acting on the bottom surface by the liquid Obtain R 30 m R

Two arms of a U tube have unequal diameters d 1 0 mm and d 1 0 cm If water surface tension 7x 10 N m is poured into the tube held in the vertical position find the difference of level of water in the U tube Assume the angle of contact to be zero Dynamics

3 A long capillary tube of radius r is put in contact with surface of a perfectly wetting liquid of density p and very low viscosity What maximum height h the liquid can rise inside the capillary Here height is measured above the level of the liquid outside the capillary Surface tension of the liquid and acceleration due to gravity are denoted by o and g respectively a h 20 pgr 20 pgr h 40 pgr b h 40 pgr d Insufficient information O 16 1 se f

34 View In English A vertical glass capillary tube open at both ends contains some water which of the following shape may be taken by water in the tube 1 3 10 O

0 5m The volume of an air bubble is doubled as it rises from the bottom of a lake to its surface If the atmospheric pressure is H m of mercury the density of mercury is n times that of lake water Find the depth of the lake

A drop of water of radius 0 0015 mm is falling in air If the coefficient of viscosity of air is 2 0 x 10 5 kg m s the terminal velocity of the drop will be The density of water 1 0 x 10 kg m and g 10 m s 1 1 0 x 10 4 m s 2 2 0 x 10 4 m s 3 2 5 x 10 4 m s 4 5 0 x 10 4 m s

For the system shown in the figure the cylinder on the left at L has a mass of 600 kg and a cross sectional area of 800 cm The piston on the right at S has cross sectional area 25 cm and negligible weight If the apparatus is filled with oil p 0 75 gm cm Find the force Frequired to hold the system in equilibrium H 600k 10000 PPPR WATANES Joper am