Fluids Questions and Answers

A capillary tube of length 50 cm is closed at both ends In contains air on both sides separated by a mercury column of length 10 cm When tube is horizontal length of air column on both sides of mercury is 20 cm When tube is made vertical length of air column are 25cm and 15cm If pressure of air in 250 250 4 4 capillary when it is horizontal is cm cm of mercury find the value of l

A venturi meter is used to measure liquid flow rate of 7500 litre min The difference in pressure across the venturi meter is equivalent to 8 m of the flowing liquid The pipe diameter is 19 cm Calculate the throat diameter of the venturi meter Assume Ca 0 96 5

Consider a ping pong ball filled with air and which is fully submerged in water due to a string which tethers it to the bottom of a full beaker What is the tension in the string What is the air pressure in the ping pong ball if it is 10 cm below the surface of the water

A solid sphere of radius R and density p is attached to one end of a mass less spring of force constant k The other end of the spring is connected to another solid sphere of radius R and density 3p The complete arrangement is placed in a liquid of density 2p and is allowed to reach equilibrium The correct statement s is are A 4R pg 3k the net elongation of the spring is C the light sphere is partially submerged 8 R pg 3k D the light sphere is completely submerged B the net elongation of the spring is

A large cylindrical vessel containing a liquid of density is kept on a horizontal surface A small spherical object of density p a is fastened to the bottom of the vessel with the help of a string as shown in the figure Neglect the viscosity and assume the gravity g vertically downwards If the vessel is now given a constant horizontal acceleration equal to g towards right then at the position of equilibrium of the spherical object with respect to the vessel the deflection of the string with the vertical is A towards left with angle tan C towards left with angle x 4 B towards right with angle 4 D towards right with angle P

6 A cylindrical tube with its base as shown in the figure is filled with water It is moving down with a constant acceleration a along a fixed inclined plane with angle 0 450 P and P are pressures at points 1 and 2 respectively located at the base of the tube Let P P pgd where p is density of water d is the inner diameter of the tube and g is the acceleration due to gravity Which of the following statement s is are correct A B 0 when a g 2 C B 2 when a g 2 2 d 0 45 g a B B 0 when a D B g 2 when a g 2

Paragraph for Questions 10 to 12 Read the paragraph carefully and answer the following questions An open rectangular tank 8mx5m x 4m initially filled with water upto height 3m is moving with a constant horizontal acceleration a along a horizontal road as shown Now answer the following questions Make g 10m s Atmospheric pressure 10 N m Density of water 10 kg m 10 The maximum horizontal acceleration amax for which water will not spill is A 1 5 m s C 3 5 m s B 2 5 m s D 4 5 m s 11 If a 5m s2 then the volume of water spilt over is A 10 m C 30 m 4 m B 20 m D 40 m 12 If a 5m s then the pressure at the centre of the bottom of the tank is A 12 105 N m 1 B 1 3 105 N m C 1 4 105 N m D 1 5x105 N m Space for rough work 8 m 3 m

A container having rectangular base filled with water is accelerating towards right with acceleration a 8 3 on a horizontal plane as shown in figure If points A B C and D are lying in same vertical plane and inside liquid choose the correct option s 1 in going from A to B pressure decrease 2 in going from A to B via D pressure first decreases then remains constant 3 in going from C to B via D pressure remains constant 4 in going from C to B via D pressure decreases V

A uniform wooden stick of length L cross section area A and density d is immersed in a liquid 4d A small body of mass m and negligible volume is attached at the lower end of the rod so that the stick floats vertically in stable equilibrium then 1 m dAL 2 m dAL 3 m dAL 2 4 m dAL 4 cont in a vertical plane Equal volumes 4d

Another liquid II which II does not mix with I is poured into one side The liquid levels of the two sides is found the same while the level of liquid I has risen by 2 cm If the specific gravity of liquid I is 1 1 then specific gravity of liquid II must be II U a 1 2 b 1 1 c 1 3 d 1 0

The pressure in a water tower is 39 877 Pascals N m higher than at an open faucet The density of water is 1000 Kg m Use Bernoulli s equation to determine the velocity of outflow from the open faucet If the height difference between the top water level in the tower and the faucet is 7 9 meters then the velocity of outflow is

Two identical balls are connected by weightless inextensible cord thrown over ideal pulley One of the balls is immersed into a vessel with a liquid With what steady velocity V in m s will the ball move if it is known that the terminal velocity acquired by a single ball in the same liquid is equal to 8 m s Resistance force is proportional to velocity The density of the liquid is p density of the material of balls is 2p 20

Due to its higher density cold water stays close to the bottom of a rectangular vessel which is filled up to the height of h 30 cm We assume that the density of water in the vessels grows linearly with increasing depth at the water level the density is equal to p 996kg m while the density p at the bottom of the vessel is unknown Determine this density using the fact ata homogeneous rod with density p 997 kg mand length h immersed in the water and fixed by one of its ends at the water level makes an angle of o 60 with the vertical Fill value of x in OMR if p 996 x

Consider a horizontally oriented syringe containing water located at a height of 1 25 m above the ground The diameter of the plunger is 8 mm and the diameter of the nozzle is 2 mm The plunger is pushed with a constant speed of 0 25 ms Then g 10 m s D 8mm A velocity of water is 4 m s B velocity of water is 8 m s C the trajectory of water leaving the syringe is a parabola D horizontal range is 2m d 2mm 1 25m

A liquid stands at the plane level in U tube when at rest If areas of cross section of both the limbs are equal what will be the difference in heights h of the liquid in the two limbs of U tube when the system is given an acceleration a in horizontal direction towards right as shown a 9 1 TT dla b La L c a a H g a d Lg a

Q7 A vertical U tube of uniform cross section contains mercury density 13 6 g cc in both arms Alcohol density 1500 Kg m column of length 0 1m is introduced into one of the arms Oil of density 0 6 g cc is poured in the other arm until the upper surfaces of the oil and alcohol are in the same horizontal level Find the length of the oil column Draw the relevant diagram 3

Q4 A wooden block with a coin placed on its top floats in water as shown in the figure The distance and h are shown there After some time the coin falls into the water Then 2002 111 Coin A I decreases and h increases B I increases and h decreases C Both I and h increase Both I and h decrease

3 5 x 4 cm s 4 4 x 5cm s FL0061 52 If the terminal speed of a sphere of gold density 19 5 kg m is 0 2 m s in a viscous liquid density 1 5 kg m find the terminal speed of a sphere of silver density 10 5 kg m of the same size in the same liquid 1 0 4 m s 3 0 1 m s 2 0 133 m s 4 0 2 m s FL0062

A Rod Inside a Capillary Tube A glass rod of diameter 1 5 mm is inserted symmetrically into a glass capillary tube of inside diameter 2 mm Now this arrangement is vertically oriented and brought in contact with the surface of water To what height will water rise in capillary Take surface tension of water is 75 x 10 3 N m and angle of contact 0

4 3 m c Up to any height b 10 m d Insufficient information 7 A piece of ice tied with the help of a thread to bottom of a cylindr container having some amount of water Length of the thread is adjusted that the ice not fully submerged Tension force in the th is 1 0 N How much and in what way will the water level in the conta shift when all the ice melts Area of the bottom of the vessel is 400 density of water is 1 0 g cm and density of ice is 0 9 g cm a 2 5 x 103 m upwards c 2 8 x 103 m upwards b 2 5 x 103 m downwards d 2 8 x 103 m downwards

tube containing liquid of density horizontally with acceleration g The pressure at A will be atmospheric pressure is Po p accelerating AB 1 Po 3pgh 3 P pgh 2h a g 2 Po pgh 4 Po 2pgh

141 The volume of an air bubble is doubled as it rises from the bottom of lake to its surface The atmospheric pressure is 75 cm of mercury The ratio of density of mercury to that of lake water is 40 3 then the depth of the lake in meter is 1 15 2 10

A block of wood is floating in water at 0 C The temperature of only water is slowly raised from 0 C to 10 C With the rise in temperature of the water Buoyant force on the block when the block will be in equilibrium increases Buoyant force on the block when the block will be in equilibrium remains unchanged The volume of block above water level first increase and then decrease The volume of block above water level first decrease and then increase

A 0 5 kg mass of lead is submerged in a container filled to the brim with water and a block of wood floats on top The lea mass is slowly lifted from the container by a thin wire and as it emerges into air the level of the water in the container drop a bit The lead mass is now placed on the block of wood As the lead is placed on the wood O Some water spills over the edge of the container O The water level rises exactly to the brim as before The water level rises but does not reach the brim of the container There is not enough information provided to decide between the three options

Two identical beakers are filled with water up to the brim On placing a wooden block in beaker 2 the wooden block floats on the surface and excess water flows out Which among beaker 1 and beaker 2 will weigh more

1 An air bubble doubles its radius on raising from the bottom of water reservoir of the surface of water in it If the atmospheric pressure is equal to 10 m of water the height of the water in reservoir is A 10 m C 70 m B 20 m D 80 m 5000

A cubical block of mass 5kg and side 10cm is pressed against a rough wall u 0 9 with a force F passing through the centre of cube inside a swimming pool as shown in the figure Then p 1000 kg m A B C D The cube will remain in equilibrium if the force F 355 9 Newton The cube will remain in equilibrium if the force is F 355 9 Newton The friction force acting on the cube is 40N if F 110 3N The friction force acting on the cube is 40N if F 50N

A bucket of water of mass 10 kg is pulled at constant velocity up to a platform 45 meters above the ground This takes 18 minutes during which time 5 kg of water drips out at a steady rate through a hole in the bottom Find the work needed to raise the bucket to the platform Use g 9 8m s2

A ball of mass m and density is completely immersed in a liquid of density p contained in an accelerating vessel as shown Select the correct answer using the codes given below the columns mg g R 6 Codes B D MEVLUDUNVAR P 4 150X init Hilafanttiin diliti may won P PATIK Pistentei Hoitotum 100 00012 and 2 3 60690504 1 force of buoyancy on ball is 2 2 2 torce of buoyancy is absent liquid particles fall with respect to vessel ball rise with respect to vessel

5 091 x 10 J The radii of two air bubbles are in the ratio 4 5 Find the ratio of excess pressure inside Also compare the works done in blowing these bubbles TROOPT Let the radii of two air bubbles be 4R 2 5R If the respective excess pressures are AP and AP2 then IT m Stocip 30oble

1 On a horizontal floor two identical cylindrical vessels A and B connected by a thin tube near their bottoms contain some water When an ice block of volume 100 cm is gently put inside the vessel A it gets half submerged in the water How much mass of water will flow through the connecting tube during the process of melting of the ice cube Density of water is 1000 kg m and density of ice is 900 kg m a 20 g c 45 g b 25 g d 50 g B

0 A tube of length L is filled completely with a incompressible liquid of mass M and closed at both the ends The tube is then rotated in a horizontal plane about one of its ends with a bo uniform angular velocity oo The force exerted by the liquid at the other end is 1 2000 2006 boil a ML 0 2 leitini 901 Ju b MLw ML 0 MLw c d

A nurse is injecting a child with 3 0 10 3 kg of vaccine With what magnitude of force assumed constant must the nurse push on the plunger of the syringe if the speed of the vaccine coming out is 1 4 m s and the length of the plunger s motion is 3 4 cm Neglect friction give your answer in newtons

ALLEN A thin liquid film formed between a U shaped wire 6 and a light slider supports a weight of 1 5 x 10 N as shown in the figure The length of the slider is 30 cm and its weight negligible The surface tension of the liquid film is 1 0 0125 N m 3 0 05 Nm 2 0 1 Nm 4 0 025 N m farger User 1 5 10 A un dira god an 30 cm 1 0 0125 Nm 3 0 05 N m Film dan d 2 0 1 Nm 4 0 025 N m

Consider a hollow pipe of infinite length and radius R The pipe has uniform distribution of charge on its surface The pipe is rotating about its axis with angular velocity The pipe is also translating with velocity v along its length There are two point P and Q as shown in the figure Point P is inside the pipe and point Q is outside the pipe Choose the correct option s V A B at point P is zero B B at point Q depends on co depends on v C B at point P P O X Q inversely proportional to distance from the axis of pipe

6 A drop of olive oil of radius 0 25mm s circular film of radius 5cm on the water surface Estimate the thickness of the film 1 8 3x10 10m 3 8 9x10 9m 2 7 2x10 9m 4 8 3x10 9m

79 If 0 is the fraction of the surface covered at PA pressure of the adsorbate A then A rate of adsorption is proportional to 0 PA B rate of desorption is proportional to 10 PA C 0 D 0 Vads at PA V max V max nt D

Water jet coming out of a stationary horizontal tube at speed v 2m s strikes horizontally a massive wall moving in opposite direction with same speed Water comes to rest relative to wall after striking Cross section of jet is 3 cm and density of water is 1 gm cc Choose the correct statement s Force exerted on the wall is 1 2 N Force exerted on the wall is 2 4 N Rate of change of kinetic energy of water jet striking the wall is 19 2 J s Rate of change of kinetic energy of water jet striking the wall is zero

00 A fixed cylindrical large cross section tank having area is filled with two liquids of densities p and 2p upto equal height h as shown in figure If a small hole is h 2 made at height from the bottom The speed of efflux will be h 1 4gh 2 3gh 3 2gh 4 gh P 2p ris h 2

A right circular cylinder open at the top is filled with liquid and rotated about its vertical axis at such a speed that half the liquid spills out then the pressure intensity at the centre of bottom is

When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body the pressure intensity varies a linearly with radial distance b as the square of the radial distance inversely as the square of the radial distance c to inversely as the radial distance

rock with density 1700 kg m is suspended from the lower end of a light string When e rock is in air the tension in the string is 48 0 N Part A What is the tension in the string when the rock is totally immersed in a liquid with density 750 kg m Express your answer with the appropriate units

If a soap bubble is given an electric charge then its radius gag m ya fagya endu faul Gidi de qua OPTIONS CLEAR SELECTION A B MARK FOR REVIEW C Increases dedi Decreases Remains same CARE Mou in

Select the correct statement s 1 Viscosity of gases Increases with Increase i Temperature 2 Viscosity of gases decreases with Increases temperature 3 Viscosity of gases may independent of temperatu 4 Viscosity of gases may Increases or decrease wi ling ung the go

Ice water and steam co exist at triple poi temperature 273 16K and pressure 4 6m Hg In a system in which the triple poi conditions of temperature and pressure exis the pressure is increased a little while keepin the temperature constant then the syste contains A ice only C steam only B water only D water and ice

A plane mirror is placed at the bottom of the tank 8 containing a liquid of refractive index P is a small object at a height h above the mirror An observer O vertically above P outside the liquid see P and its image in the mirror The apparent distance between object its image will be 0 1 2 h 3 2h 2h H 4 h 1 2 134a tin i n sa v t v i a h fra 2 1 2 h 3 af from 2h 31 30 2 atd 341 1 h

hi A uniform wooden plank cuboid is floating on water is tied to the bottom of the pool such that in static equilibrium the diagonal plane of symmetry of its vertical cross section coincides with the level surface of water as shown in figure The specific gravity of the wood is

A cubical block of density P side length a is just immersed in liquid with density p in a large container as shown by applying a force F If the force F is removed at t 0 then the height in m above the surface of the liquid to which centre of mass of the block will rise is Given that a 2m neglect the effect of surface tension F p 4 a H

A parallel sided block of glass of refractive index 2 which is 40 mm thick rests on the floor of a tank which 4 is filled with water w 3 The difference betweer apparent depth of floor at A and B when seen from vertically above is equal to

20 A steel ball is released just below the surface of thick oil in a cylinder During the first few centimetres of travel what is the acceleration of the ball A constant and equal to 10 m s B constant but less than 10 m s C decreasing D increasing