Fluids Questions and Answers

Calculate the life time of a soap bubble of radius R connected with the atmosphere through a capillary of length 1 and radius r The surface tension is S and coefficient of viscosity of air is n c a 6 R c 4 b 2n R4 Sr Sp 4 Sr4 2n R4 d 65r4 MIRA

Illustration 5 31 A sliding fit cylindrical body of mass of 1 kg drops vertically down at a constant velocity of 5 cm s 1 Find the viscosity of the oil Strea Oil 14 9 cm 1 kg 15 cm 15 cm

27 If in limbs of venturimeter height difference is 20 cm then find velocity of fluid flow 3 30cm 1 0 22 m s vid blow 2 0 15 mla 20cm 10cm ng taggedbon 2 0 33 m s CANOS

The spring balance A read 2 kg with a block m suspended from it A balance Breads 5 kg when a beaker with liquid is put on the pan of the balance The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in fig In this situation A The balance A will read more than 2 kg B The balance B will read less than 5 kg C The balance A will read less than 2 kg and B will read more than 5 kg D The balance A and B will read 2 kg and 5 kg respectively

If a capillary is radius r is dipped in water the height of water that rises in it is h and its mass is M If radius is made four times then mass of water that will rise in capillary will be 1 4M 2 2M 3 M 4 M 2

6 An ice cube contains a large air bubble The cube is floating on the horizontal surface of water contained in a trough What will happen to the water level when the cube melts 1 It will remain unchanged 2 It will fall 3 It will rise 4 First it will fall and then rise

A ball floats on the surface of water in a container exposed to the atmosphere If the container is now covered and the air is pumped out then A the ball will remain at its former depth B the ball will rise somewhat C the ball will sink to the bottom D the ball will sink a bit

relative density of wooden piece 1516 3 A piece of wood of uniform cross section and 15 cm height sinks 10 cm in water and 12 cm in spirit Find the relative densities of wood and spirit 4 A block of wood is kept on a tabletop The mass of wooden block is 5 kg and its dimensions are xorted by the wooden block on the tabletop if it is made

Single 7 1 A U tube of base length filled with same volume of two liquids of densities p and 2p is moving with an acceleration a on the horizontal plane If the height difference between the two surfaces open to atmosphere becomes zero then the height h is given by L A l B 3a 2g l 860 g a

13 Containers A B and C of equal volume contain oxygen neon and methane respectively at the same temperature and pressure The correct increasing order of their masses is a A B C c C A B 14 Average volume available to a molecule in a sample of a gas at STP is a 1 66 x 10 24 cm c 22400 cm b 3 72 x 10 20 cm d unpredictable 15 Pressure of a mixture of 4 g of O and 2 g of H confined in a bulb of 1 litre at 0 C is b 31 205 atm 105 a 25 215 atm c 45 215 atm d 15 210 atm 16 Which of the following volume V temperature T plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure V L V L 4 22 4 L 273 K V L A 2105 is to 22 4 L 273 K b B C A d C B A to 1012 36 8 Ls 373 K a 22 4 L 273 K T K V L 4 2100 125 30 6 L3 B 373 K te c 22 4 L 273 K ban 28 6 L 373 K b T K T K mov d is T K Kerala PET 2007 AIIMS 2005 17 Containers A and B have same gas Pressure volume and temperature of A are all twice that of the number of molecules of A 14 2 L 373 K

A wooden block and a metal coin are connected by a string as shown in figure Both have same volume and both are placed in a beaker of water Now the beaker is given acceleration towards right then the string will tilt towards 1 Right 2 No where 3 Left 4 Either right or left

11 Relative density of silver is 10 8 What is the density of silver in SI unit 5 izomm vlous 12 While floating in water part of volume of a wooden piece is immersed in water What is the 6 relative density of wooden piece 13 A piece of wood of uniform cross section and 15 cm height sinks 10 cm in water and 12 cm in

126 For amongst the following curves which one shows the variation of velocity with time t for small sized spherical body falling vertically in a long column of viscous liquids 1 V4 1 3 2 4 V4 VA

100 ml A metallic sphere of density 5 g cm 3 is pro jected upward from the bottom of a pond with a velocity 10 m s The velocity of the sphere on reaching the surface of the water is found to be 8 m s Determine the pressure exerted by water at the bottom of the pond Neglect the viscous force acting on the sphere T M

The mass of a body is 70 kg When completely immersed in water it displaces 2000 cm water What is the relative density of the material of the body

Example 16 17 Water flows through the tube as shown in figure The areas of 2 cm respectively The rate of flow of water through the tube is 500 cm Is Find cross section of the wide and the narrow portions of the tube are 5 cm and the difference of mercury levels in the U tube 2 Fig 16 56

A solid sphere falls into a viscous AP liquid from a large height Which of the graphs shown best represents the variation of velocity of sphere in liquid with time a P c R b Q d S P

6 The mass of a copper piece is 44 g A measuring cylinder contains water to a level of 12 mL The water level rises to 17 mL mark when the copper piece is dipped in the measuring cylinder Find i the volume of copper piece and ii the density of copper when and 5 the r Solution bottle M Mas Mas

5 The length of one edge of a glass plate of thickness 0 2 cm is 9 8 cm If this edge of the glass plate touches the surface of a liquid of surface tension 60 dyne cm then it is pulled down with a force of Assume that angle of contact to be zero 1 1100 dyne 3 1000 dyne 2 2400 dyne 4 1200 dyne

Che er 1 22 A capillary tube of radius 0 50 mm is dipped vertically in a pot of water Find the difference between the pressure of the water in the tube 5 0 cm below the surface and the atmospheric pressure Surface tension of water 0 075 Nm

A mercury manometer figure 24 W1 consists of two unequal arms of equal cross section 1 cm and lengths 100 cm and 50 cm The two open ends are sealed with air in the tube at a pressure of 80 cm of mercury Some amount of mercury is now introduced in the manometer through the stopcock connected to it If mercury rises in the shorter tube to a length 10 cm in steady state find the length of the mercury column risen in the longer tube 10 cm 05 locm

1 A cylindrical log of wood floats vertically in water with one fourth of its length out of water The density of wood is A 0 25 g cc B 0 5 g cc D 1 g cc C 0 75 g cc

A tube filled with water rotating with angular velocity w Find equation of curve so formed 5 cm 10 cm 5 cm Ans V 2x

B A tank with a square base of area 2 m is divided into two compartments by a vertical partition in the middle There is a small hinged door of face area 20 cm at the bottom of the partition Water is filled in one compartment and an acid of relative density 1 53 x 10 kg m 3 in the other both to a height of 4 m The force necessary to keep the door closed is Take g 10 m s d 80 N c 40 N a 10 N b 20 N

24 A hemisphere of volume v is kept in a liquid of density p as shown in figure Vertical thrust on the hemisphere due to liquid inside it is 1 vpg 3 vpg A 0 1 1 1 8 2 8 9 8 6 0 2 2 vpg 4 Zero

13 A large open tank has two holes on the side wall One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top When the tank is completely filled with water the quantities of water flowing out per second from both the holes are the same Then R is equal to 1 2nL 3 L 2 4 L 2 L 2 A

20 The cylindrical tube of a spray pump has radius R One end of it has n fine holes each of radius r If the speed of liquid in the tube is v the speed of the ejection of the liquid through the holes is 1 2 3 v R nr VR n r VR nr

As raindrops fall in the air starting from rest a Its velocity and acceleration both increases b Its velocity increases and acceleration decreases c Both velocity and acceleration first increases then decreases d None of these

A fisherman hooks an old log of wood of weight 12 N and volume 1000 cm He pulls the log half way out of water The tension in the string at this instant is a 12 N b 8 N c 10 N d 7N When an incompressible liquid jet flowing in a pipe reaches a narrow cross section from a wider one its

A beaker filled with water is at rest in a car that accelerates to the right with an acceleration 5m s A simple pendulum of length 1 5 has a small wooden bob with the wood s specific gravity s 0 8 is fixed to the floor of the beaker as shown in the diagram 1 Find the angle made by the string with the vertical Will the string tilt towards right or towards left

Two pieces of metal when immersed in a liquid have equal upthrust acting on them then a Both pieces must have equal weights b Both pieces must have equal densities c Both pieces must have equal volume d Both are floating to the same depth A fisherman hooks an old log of wood of weight 12 N and volume 1000 cm He pulls the log half way ou

A container has a hole at a height of 2m If the time taken by the efflux to strike the inclined plane perpendicularly is 1 sec Then the height of liquid level from floor initially is Take g 10 m s Area of tank is very large in comparison with area of hole 2m

08 Cylindrical bucket B with water in it has mass 10 kg balances a mass of 12 kg A on horizontal surface as shown in the figure A place of cork of mass m 2 kg and specific gravity 0 5 is tied to the bottom of the bucket through a light string A is moved horizontally with constant velocity 4 m s as shown Find the ratio of tension T and T at the instant A reaches point C T 1 B 60 A TA 1 m

2 111 A block of mass 10 kg connected to another hollow block of same size and negligible mass by a spring of spring constant 500 N m floats in water as shown in the figure If the compression in the spring is 2 N cm then find the value of N Pwater 1 10 kg m g 10 m s m 10 kg

0 105 The velocity distribution in a viscous flow over a plate is given by u 4y y for y 2m where u velocity in m s at a point distant y from the plate If the coefficient of dynamic viscosity is 1 5 in SI units determine the shear stress at y 0 in N m

0 9 m cross section A is bent to form a circular arc of radius R forming three quarters of a A tube of circle A liquid of density p is flow through the tube with a linear speed v as shown in the figure The net force exerted by the liquid on the tube is A pAv B 1 TAV 4 90 C 2 pav D zero 205

A cubical block is floating in a liquid with one third of it s volume immersed in the liquid When the whole system accelerates upwards with acceleration of g 2 A The fraction of volume immersed in the liquid will change 4 B The buoyancy force on the block will change C The buoyancy force will increase by 50 percent D The pressure in the liquid will increased in metallic shell s of radius R and 2R out of which the inner shell is having charge O

densities P P and P2 A large tank is filled with two immiscible liquids of A small hole is made at the base of the tank and the liquid of density p starts flowing out of it Three points A B and C are m rked on a vertical line Bernoulli s equation can be applied A B C D A P B P C h h Only at points A and C Only at points B and C At any two points A B and C None of these

A coaxial cylinder made of glass is immersed in liquid of surface tension S Radius of inner and outer surface of cylinder are R and R respectively Then the rise of liquid between the cylinders is Density of liquid is p

3 2 x 10 J 4 1 10 J In Poiseuilli s method of determination of coefficient of viscosity the physical quantity that requires greater accuracy in measurement is 1 Pressure difference 3 Length of the capillary tube 2 Volume of the liquid collected 4 Inner radius of the capillary tube tube The velocity distribution of the fluid is best represented by th zutta

An oil of viscosity 0 5 stoke is flowing through a pipe of 30cm in diameter at the velocity of 4 52meter per second find reynolds number 1 stoke 10 4 m 2 per second and density of oil is 0 9 27 120 27 220 26 500 27 750

J What is the velocity of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one half that of a freely falling body The densities of metal and of liquid are p and a respectively and the viscosity of the liquid is n 1 p 20 2 r g 20 0 91 911 pm cross section area is hang from rigid end When weight of 1 kg is hung from it then 3 p 21 8 p 0 91 4

A small sphere of radius r falls from rest in a viscous liquid As a result heat is produced due to viscous force Th rate of production of heat when the sphere attains its terminal velocity is proportional to 1 r 2 r NEET 2018 3 r 4 r

In a capillary tube experiment a vertical 30 cm long capillary tube is dipped in water The water rises up to a height of 10 cm due to capillary action If water temperature increases then the new height of water column in capillary becomes A B 30 cm D greater than 10 cm Cequal to 10 cm less than 10 cm Correct Answer

A solid sphere of mass m 2 kg gravity s 0 5 is held stationary relative to tank filled with water by attaching a string between sphere and bottom of the tank The tank is accelerated upward with acceleration 2 m s2 The tension in the string is p 1000 J15 24 N 2m b a my kg 2 4 N m a 2 m s

10 A semicircular glass tube filled with water containing an air bubble is sealed at its ends If the tube is held with its plane vertical and made to move in its plane with a constant acceleration the bubble stays aside of the highest point as shown in the figure What can you conclude about acceleration vector of the tube a It points towards the left c Its magnitude is g tan0 b It points towards the right d Its magnitude is gcot 0 Fluid Mechanics Vertical 0 Centre 7 5

Question 13 and 14 are based on the following physical situation An ideal liquid of density p is filled in a horizontally fixed syringe fitted F with piston There is no friction between piston inner surface of the syringe Cross section area of the syringe is A An orifice is made at one end of the syringe When the piston is pushed into the syringe the liquid comes out of the orifice and then following a parabolic path falls on the ground With what velocity does the liquid come out of the orifice 2F pA F pghA PA a c VpA F 2pghA PA 6 d

6 If a capillary is radius r is dipped in water the height of water that rises in it is h and its mass is M If radius is made four times then mass of water that will rise in capillary will be 1 4M 3 M 2 2M 4 M 2

A U tube having horizontal arm of length 20 cm has uniform cross sectional area 1 cm It is filled with water of volume 60 cc What volume of a liquid of density 4 g cc should be poured from one side into the U tube so that no water is left in the horizontal arm of the tube 1 60 cc 3 50 cc 2 45 cc 4 35 cc

A fire hydrant delivers water of density p at a volume rate L The water travels vertically upward through the hydrant and then does 90 turn to emerge horizontally at speed V The pipe and nozzle have uniform cross section throughout The force exerted by the water on the corner of the hydrant is S L SULI