Fluids Questions and Answers

49 A tube of small uniform cross section is used to siphon the water from the vessel Then choose the correct alternative s Pwater 103kg m g 10 m s Patm 105 Pa A h c both are correct d both are wrong 4m B a Water will come out from section B with a velocity of 80 m s b The greatest value of h for which the siphon will work is 10 m

7 31 To measure the atmospheric pressure four different tubc3 of length 1m 2m 3m and 4m are used If the height of the mercury column in the tubes is h h h3 ha respectively in the four cases then h h hh is A 1 2 3 4 C 1 2 2 1 B 4 3 2 1 D 1 11 1

54 Air is blown through a pipe AB at a rate of 15 liters per minute The cross sectional area of the broad portion of the pipe AB is 2 cm and that of the narrow 2 portion is 0 5 cm2 The difference in water level h is Pair 1 32 kg m a 5 26 mm c 4 38 mm A RRE B water b 1 54 mm d 3 26 mm

7 19 Figure 7 102 shows a hydraulic press with the larger piston of diameter 35 cm at a height of 1 5 m relative to the smaller piston of diameter 10 cm The mass on the smaller piston is 20 kg What is the force exerted on the load by the larger piston The density of oil in the press is 750 kg m Takes g 9 8 m s 1 5 m 20 kg

1 An iron block is on a boat which floats in a pond The block is thrown into the water The level of water in the pond will be a equal to the earlier level b less than the earlier level c more than the earlier level d depends on how large the block is

7 26 For a fluid which is flowing steadily the level in the vertical tubes is best represented by JL A C JE B D 7 27 A cylindrical wooden float whose base area S and the A E C E 7 31 of le merc four A C

d both are wrong 50 There are three different liquids with densities P1 P2 and p3 in a U shaped container as shown in figure The lengths shown are H 15 cm and H 10 cm Which of the following equations gives the correct relation between the densities of the fluids in the container a 3p3 2p1 P2 c 2p3 3p1 P2 P3 H H P2 P b p3 2p1 3p2 d p3 3p1 2p2

ty of work P2 are em ect he 51 53 The diagram shows a tall cylindrical container kept on a horizontal surface From a tap water comes with constant rate q m s Initially the container was empty An orifice of area of cross section A is made at 3 in the side wall of the container If the some height horizontal range of the water jet in steady state is found to be 2h then the relation between h and q is 9 a h 94 39 29A2 c h Ain is b h d h 9 2gA 29 942 Sinarge a Vpog 4 B More t 1 A samples and 120 a metal c liquid 2 Water is 3 a m s of the t is prop a a 3 Equa

c 2p3 3p1 P2 d p3 51 A solid sphere of radius r is floating at the interface of two immiscible liquids of densities p and P2 P2 P1 half of its volume lying in each The height of the upper liquid column from the interface of the two liquids is h The force exerted on the sphere by the upper liquid is atmospheric pressure Po and acceleration due to gravity is g 2 c 3 Solid sphere P19 PI 2 2 a p rr hr p g b h p 9 P19 3 d Pox r P2

52 A hollow sphere of volume V is floating on water surface with half of its volume immersed What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water a V 2 c V 4 b V 3 d V

37 A vertical jet of water coming out of a nozzle with velocity 20 m s supports a plate of mass M stationary at a height h 15 m as shown in the figure If the rate of water flow is 1 litre per second the mass of the plate is Assume the collision to be perfectly inelastic a 1 kg c 2 kg M 15 m v 20 m s b 2 kg d 4 kg CE

Half of the rectangular plate shown in figure is made of a material of density p and the other half of density p2 The length of the plate is L The distance of centre of mass of the system from O is K O C L

7 49 The interface of two liquids of densities p and 2p respectively lies at the point A in a U tube at rest The height of liquid column above A is 8a 3 where AB a The cross sectional area of the tube is S With what angular velocity the tube must be whirled about a vertical axis at a distance a such that the interface of the liquids shifts towards B by 2a 3 A 8a 3 2p ALT BER

An open cylindrical vessel of large cross section A contains liquid upto a height H 120 cm A A small orifice of area at a height of 1000 h 20 cmis opened There is a plate PQ of length 60 cm at a distance 20 cm from tank on the base level g 10 m s H h

is flowing in a tube as shown in figure Area of section 1 is double that of section 2 Centre of mass of section 2 is h height above the Centre of mass of section 1 and level of water in tube 1 is h height above that in tube 2 Then Tube 1 O O O Section 1 Section 2 Velocity of fluid at section 1 is Tube 2 Velocity of fluid at section 1 is gh 3 2gh 3 Work done by gravitational force per unit volume from section 1 to section 2 is pgh Work done by elastic forces pressure per unit volume

7 55 A wooden plank of length 1m and uniform cross section is hinged at one end to the bottom of tank as shown in figure 7 118 The tank is filled with water upto a height of 0 5 m Find the angle that the plank makes with the vertical in the equilibrium position Exclude the case 0 0 sr no Ee sball

2 45 A block of wood weighs 12 kg and has a relative density 0 6 It is to be in water with 0 9 of its volume immersed What weight of a metal is needed a if the metal is on the top of wood b if the metal is attached below the wood RD of metal 14

1 point The tank in the form of a right circular cone of radius 6 feet and height 14 feet standing on its end vertex down is leaking through a circular hole of radius 3 inches Assum the friction coefficient to be c 0 6 and g 32 ft s Then the equation governing the heigh h of the leaking water is dh dr If the tank is initially full it will take it seconds to empty

7 51 A wooden stick of length L radius R and density p has a small metal piece of mass m of negligible volume attached to its one end Find the minimum value for the mass m in terms of given parameters that would make the stick float vertically in equilibrium in a liquid of density o

The velocity of liquid flowing through a tube at certain distance from the axis of tube A increases with distance B remains constant C decreases with distance D depends upon length of the tube

A spherical steel ball of mass 40 g and density 8 10 kg m is dropped into a column of a liquid of density 2x10 kg m At the instant when the velocity of the ball is half of its terminal velocity the force of viscosity acting on the ball is N g 10 m s Answer Enter your answer here

4 A container of square base of dimension 10 cm 10 cm and of sufficiently long height contains a liquid upto a height 30 cm as shown in figure The minimum horizontal acceleration of the container such that the pressure at point A becomes atmospheric is 30 cm 1 10 g 3 1 a 10 cm A 10 cm 2 6 g a Pal

A large weather balloon whose mass is 226 kg is filled with helium gas until its volume is 325 m Assume the density of air is 1 2 kg m and the density of helium is 0 179 kg m What additional mass can the balloon support in equilibrium 3

23 A tube 1 cm in cross section is attached to the top of a vessel 1 cm high and cross section 100 cm Water fills the system upto a height of 100 cm from the bottom of the vessel The force exerted by the liquid at the bottom of the vessel is excluding atmospheric pressure force g 10 m s 1cm a 1000 N c 900 N 100cm 99cm 1cm b 990 N d 100 N

iter at 5 C p 1000 kg m3 and 1 002 10 3 kg m s is flowing through a 0 3 cm diameter and 9 m long horizontal pipe steadily at an average velocity of 1 m s Determine the head losses across the pipe 1 99 m 2 72 m 1 12 m 2 95 m

a 75 b 30 19 A small hole is made at the bottom of a symmetrical jar as shown in figure A liquid is filled into the jar upto a certain height The rate of fall of liquid is independent of the level of liquid in the jar Then the surface of jar is a surface of revolution of the curve ya y kx4 c y kx X b y kx d y kx5

46 Figure shows a siphon Choose the wrong statement h 0 h a Siphon works when h 0 b Pressure at point 2 inside the tube is p2 Po pgh c Pressure at point 3 is po d None of the above Po atmospheric pressure d

22 Two spheres of volume 250 cc each but of relative densities 0 8 and 1 2 are connected by a string and the combination is immersed in a liquid The tension in the string is g 10 m s2 fed fe a 5 0 N b 0 5 N c 1 0 Nisou d 2 0 N

1000 42 An open cubical tank was initially fully filled with water When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water was spilled out The acceleration was a g 39 b 2g 3 c g 2 d g 4

24 In the arrangement shown in figure mB ratio of density of block B and of liquid is 2 1 The system is released from rest Then A and the a block B will oscillate but not simple harmonically b block B will oscillate simple harmonically c the system will remain in equilibrium d None of the above

A flat plate moves normally with a speed v towards a horizontal jet of water of uniform area of cross section The jet discharges water at the rate of volume V per second at a speed of v The densit of water is p Assume that water splashes along the surface of the plate at right angles to the origina motion The magnitude of the force acting on the plate due to jet of water is A pVv 1P B P V V pV V V D pV v v

43 Some liquid is filled in a cylindrical vessel of radius R Let F be the force applied by the liquid on the bottom of the cylinder Now the same liquid is poured into a vessel of uniform square cross section of side R Let F2 be the force applied by the liquid on the bottom of this new vessel Neglect atmosphere pressure Then c F F d F F a F F b F F2 TC

29 A vertical capillary is brought in contact with the water surface surface tension T The radius of the capillary is r and the contact angle 0 0 The increase in potential energy of the water LUE density p is a independent c independent of p of T b independent of r d zero

15 A cubical block of wood of edge a and density p floats in water of density 2p The lower surface of the cube just touches the free end of a massless spring of force constant k fixed at the bottom of the vessel The weight W put over the block so that it is completely immersed in water without wetting the weight is a a a pg k b a apg 2k d 1 a a pg h 2 a ap9 2k 2 c a

4 A cylinder of mass m and density p hanging from a string is lowered into a vessel of cross sectional area s containing a liquid of density o p until it is fully immersed The increase in pressure at the bottom of the vessel is a mpg OS b mg S 1in12 01 c mog ps d zero

18 A glass tube 80 cm long and open at both ends is half immersed in mercury Then the top of the tube is closed and it is taken out of the mercury A column of mercury 20 cm long then remains in the tube The atmospheric pressure in cm of Hg is assume temperature to be constant a 75 b 30 c 60 d 90

12 What is the height to which a liquid rises between two long parallel plates a distance d apart Surface tension of liquid is T and density is p 4T 2T a pgd T pgd c b d pgd T 2pgd

8 A solid ball of density p and radius r falls vertically through a liquid of density p2 Assume that the viscous force acting on the ball is F kru where ki a constant and v its velocity What is the termina velocity of the ball a c 2 4ngr P P 3k 2ng P1 P2 3gr k 2 r P P 3gk d None of these b

16 The opening near the bottom of the vessel shown in figure has an area A A disk is held against the opening to keep the liquid from running out Let F be the net force on the disk applied by liquid and air in this case Now the disk is moved away from the opening a short distance The liquid comes out and strikes the disk inelastically Let F2 be the force exerted by the liquid in this condition Then F 1 F2 is 1 a b 1 c IN 2 AIWA h d 1

10 Check the correctness of the relation h rpg fo 2S the height of a liquid of density p and surface tensio S raised in a capillary tube of radius r and angle contact zero with the liquid If incorrect then dedu the correct form Ans h 2S r p

11 A drop of water of mass m and density p is placed between two well cleaned glass plates the distance between which is d What is the force of attraction between the plates T surface tension 4Tm a Tm 2po2 b pd fej 2Tm pd Tm pq d

The surface tension of soap solution is 0 03 N m The work done in blowing to form a soap bubble of surface area 40 cm is Question Type Single Correct Type 1 1 2 x 10 4j 2 2 4 x 10 4J 3 12 10 4J A 2110 4

Uniform speed of 2 cm diameter ball is 20 cm s in a viscous liquid Then the speed of 1 cm diameter ball in the same liquid is Question Type Single Correct Type 1 2 5 cms 1 10 cms 1 3 40 cms 1

A swimming pool is 10 m wide and 20 m long and its bottom is an Inclined plane the shallow end having a depth of 1 m and the deep end 3 m If the pool is full of water find the hydrostatic force on the following Round your answers to the nearest integer a the shallow end 312 5 XN b the deep end 2812 5 c one of the sides 2500 N N d the bottom of the pool 25125 XN

A barometer when accelerated vertically up by acceleration a gives the reading as 63 33 cm of Hg Find the value of a if atmospheric pressure is 76 cm of Hg 1 2 m s 3 4 m s 2 3 m s 4 5 m s

A particle of mass 1 kg is fired with velocity 50 m s at an angle of 60 from horizontal It is acted by viscous force of 0 2v during its journey The horizontal distance travelled by it in first 10 seconds

fluid of density p is rotated with a certain angular velocity in a cylindrical v ion 1 R 2h The angular velocity is w The angular velocity is w The kinetic energy of fluid is 2gh R 4gh R 16mpgh R 15

0 A cubical block of edge length a floats in a liquid of density p such that fraction of volume immersed is b Calculate the minimum force which should be applied on the block such that it just immerses fully in the liquid 1 a pg 1 b 2 b pg 1 a 3 a b pg 4 a bpg

A container contains some liquid of density twice that of Hg A bubble moves from bottom of the container to the surface of the liquid such that the radius of the bubble doubles Find the height of the liquid in the container if atmospheric pressure is 76 cm of Hg column 1 266 cm 3 152 cm 2 76 cm 4 228 cm

In a certain gravity free space the piston of an injection is being pushed so that the water jet comes out with a constant speed v The area of the piston is much greater than that of the orifice of the injection A The force required to be applied on the piston is proportional to v B The power developed by the force pushing the piston is proportional to v C The time for emptying the injection is proportional to v D The total work done in emptying the injection is proportional to v