Fluids Questions and Answers

A false statement is 1 Angle of contact 0 90 if cohesive force adhesive force 2 2 Angle of contact 0 90 if cohesive force adhesive force 2 3 Angle of contact 0 90 if cohesive force adhesive force 2 4 If the radius of capillary is reduced to half the rise of liquid column becomes four times

Two spherical soap bubbles of radii r and r in vacuum combine under isothermal conditions The resulting bubble has a radius equal to mathione criathong mathongo 1 2 TIT2 11 12 4

4 inversely proportional to h Two drops of equal radius are falling the 060 6 with a steady velocity of 5 cm s If the two drops coalesce then its terminal velocity will be 1 4 x 5cm s 2 4 cm s 3 5 x 4 cm s 4 4 x5cm s

The velocity of propagation of waves V in a shallow liquid depends on the liquid depth h gravity g surface tension o units of N m and liquid density p Using the pi theorem method find an expression for V V th

30 A cylinder is filled with a liquid of density d upto a height h If the beaker is at rest then the mean pressure on the wall is 1 Zero 2 hdg 4 2 hdg

7 A light cylindrical vessel is kept on a horizontal surface Its base area is A A hole of cross A section is made on the side wall just at its 50 bottom Minimum coefficient of friction such that it does not slide due to thrust force of emerging liquid is 1 0 04 2 0 5 3 0 2 4 0 08 f fames f

Awooden block with a coin placed on its top Floats in water as shown in Figure The distance I and h are shown in the figure After some time the coin falls into the water Then Cotn 1 I decreases 2 h decreases 3 1 increases 4 Both 1 and 2 h

A particle is suspended from a fixed point by a light inextensible thread of length 7 With what velocity the particle must be projected horizontally from its lowest point so that it leaves the circular path at an angle 120 with vertical 1 5gl 3 5gl 2 4 3gl 2 7gl

A wooden block of density 0 5 g cc is tied to a string The other end of the string is fixed to the bottom of a tank The tank is filled with a liquid of density 1 g cc If the tension of the string is 20 N then the mass of the block is Take g 10 m s

51 A body floats in water with its one third above the surface The same body floats in a liquid with one third volume immersed The density of the liquid in kg m is 1 9000 3 3000 2 2000 4 1500

9 A wooden block is floating with some part immersed in water If the vessel moves upward with an acceleration a then the fraction immersed in water will 1 Increase 2 Decrease 3 First increase then decrease 4 Remain same

27 An air bubble of radius r in water is at certain depth below the water surface If P is the pressure inside the bubble then the depth below the water surface is Po Atmospheric pressure p Density of water T surface tension of water 2701 3 P P 27 0 pg rpg P P 2T roa 2 4 P Po pg a 2T rpg P P T 2rog

A sphere of uniform density floating in a glass of wat refer to figure can be at any distance from axis of glass Q Where will be the sphere located after sufficien large time if glass is rotating with constant angular velocity a

16 A soap bubble is having internal a external radii as R and 2R respectively surface tension of soap solution is T the excess pressure inside bubble will b SOL NCERT Pg 26 dical 1 2 3 3T ce 2T R

If two liquids of same masses but densities P and P2 respectively are mixed then density of mixture is given by a p c p P P 2 2P1P2 P P b p d p P P 2P P2 P1P2 P P

18 A piece of solid weighs 120 g in air 80 g in water and 60 g in a liquid The relative density of the solid and that of the liquid are respectively 1 3 2 3 21 2 3 2 2 4 3 24 A wo float dista time

Multiple Answer type questions 11 If copper floats on mercury and gold sinks in mercury then which is false a copper is less denser than gold b mercury has least density among the three metals mercury is denser than gold copper is more denser than mercury ntatement is correct 105

Two light bodies are kept floating on the surface of water very close to each other as shown below Water surface takes different shapes depending on the surface nature of the bodies Identify true situations from the following arrangement

A beaker filled with liquid is placed in the pan of a spring balance If you dip your finger in it the reading of the balance will be 1 increased 2 unchanged 3 decreased 4 may increase or decrease according to the nature of liquid

A spherical raindrop of radius R is moving down in air with terminal velocity 2 m s If it clubs with another identical raindrop then the larger drop will have the terminal velocity 1 22 3 m s 3 24 3 m s 2 2 m s 4 25 3 m s

Q 11 Height of mercury in a barometer is h 76 0 cm at a temperature of 8 20 C If the actual atmospheric pressure does not change but the temperature of the air and hence the temperature of the mercury and the tube rises to 8 35 C what will be the height of mercury column in the barometer now Coefficient of volume expansion of mercury and coefficient of linear expansion of glass are 8 x 10 40 1

The diameter of the sphere is 2 mm Calculate the value of the Reynolds number for the sphere with 2 mm of diameter when it is moving with a speed of 0 05 m s The value of viscosity is 12 N s m and the value of density is 1300 kg m A 0 01 B 2 C 1 D 0 5

A lower end of a glass capillary tube is dipped in water Water rises to a height of 8cm The tube is then broken at a height of 6cm The height of water column and angle of contact will be heig 1 6cm sin 3 4cm sin 3 4 2 3 2 6cm cos 1 4 4 4cm cos 12

8 A periodic external force acts on a 6 kg mass suspended from the lower end of a vertical spring of force constant 150 Nm The damping force is proportional to the instantaneous speed of the mass and is 80 N when speed is 2 ms calculate the resonance frequency 1

3 1 6 10 m 4 1 6 10 m 11 A horizontal pipe line carries water in a stream 11 line flow At a point along the pipe where the cross sectional area is 10 cm the water velocity is 1 ms and the pressure is 2000 Pa The pressure of water at another point where the cross sectional area is 5 cm is 1 400 Pa 2 500 Pa 3 1 6 x 10 m 4 1 6 10 m ur t an eri tefta vare ti facit for at and gut 10 m 2000 Pa Teft facit ut face and sm and are 1 400 Pa 2 500 Pa

The neck and bottom of a bottle filled with liquid are 2 cm and 12 cm in radius respectively If the cork is pressed with a force of 15 N in the neck of the bottle then force exerted on the bottom of the bottle is 460 N 15 N 660 N 540 N

3 8 identical drops of the same radius are fall through air with steady velocity 5 cm s If these drops coalesce the terminal velocity would be 10 m s 2 0 1 m s 3 20 cm s 4 40 cm s

An ice block floats in a liquid whose density is les than water A part of block is outside the liquid When whole ice has melted the liquid level will 4 Rise 2 Go down Joy Remain same

A uniform solid sphere floats in an immis mixture of water Pw 103 kg m liquid p 13 50x10 kg m such that its portion is in water and Density of metal is 1 4 5 103 3 3 5 103 kg m kg m th portion is in 2 4 0 103 A 1 9 10 ko EE

Rain drop is falling under gravity on the earth surface Its velocity remain constant near the earth surface this constant velocity is known as terminal velocity This velocity depends on viscosity of air no radius of drop ro difference in density of water and air do and acceleration due to gravity g Then terminal velocity may be Given that F 6 V A VT C 2 rogo 9 no 29 2 go do B 11 R VT 2 rono 9 g 2 g do

A large tank of height h 4m water has a hose connected to it as shown in figure The tank is sealed at the top and has compressed air between the water surface the top When the water height h is 3m the gauge pressure of air is P 1 10 N m Assume that the air above the water surface expands isothermally What is the velocity of flow out of the hose when h has decreased to 2m Assume ideal fluid flow P 10 N m atm m h 4m P h lm

An ideal gas is trapped between a mercury column and the closed end of a narrow vertical tube of uniform base containing the column The upper end of tube is open to atmosphere at atmospheric pressure 76 cm of mercury The length of mercury column and trapped air column are 20 cm and 43 cm respectively If the tube is tilted slowly in a vertical plane to an angle 30 with horizontal find the length of air column assuming no change in temperature

A rectangular narrow U tube has equal arm lengths and base length each equal to The vertical arms are filled with mercury up to 1 2 and then one end is sealed By heating the enclosed gas all the mercury is expelled If atmospheric pressure is Po the density of mercury is p and cross sectional area is S then Neglect thermal expansion of glass and mercury 50 A Work done by the gas against the atmospheric pressure is PS 2 7 B Work done by the gas against the gravity is S Spg C Work done by the gas against the atmospheric pressure is P SC D Word done by the gas against the gravity is Spg

solid uniform ball of volume V floats on the interface of two immiscible liquids The specifi avity of the upper liquid is y 2 and that of the lower liquid is 27 where y is the specific gravity a e solid ball The fraction of the volume of the ball that will be in upper liquid is 2v V

5 A uniformly charged soap bubble of radius r is in equilibrium with air pressure inside and outside equal If T is the surface tension of soap solution the potential of the soap solution is 1 4Tr Eo 2Tr 2 8Tr VEO Tr

Answer of both question are different why Acc to me an wer of both question is h 2 4 In a vertical capillary of height h water rises upto complete height h If the capillary is tilted at 30 with horizontal then the height upto which water will rise becomes 1 h 3 2h 3 3 2 h 4 Q 3 the length of water column inside the capillary becomes 1 h 2 h 4 2 214 h h NI2 3h

43 Two containers A and B are partly filled with water and closed The volume of A is twice that of B and it contains half the amount of water in B If both are at the same temperature the water vapour in the containers will have pressure in the ratio of b 1 1 d 4 1 Xa 1 2 c 2 1 CBSE PMT 88

erties of Fluids 217 31 The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after some time If the density of glycerine is d the viscous force acting on the ball is 2 d 1 01 2 d 1 Mg 1 3 mald d 2 Mg d d 4 mad d

4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure The radius of vessel is 5 cm and the angular speed of rotation is o rad s The difference in the 1 height h in cm of liquid at the centre of vessel and at the side will be 10 cm h

Given the density of the aqueous solution is 1 00 g mL and it has a specific heat capacity of 4 18 J g C same as water calculate the heat transfer q in this reaction q mc t units will be joules J

2 IfM 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 2019 Main 9 April 1 a 2M d M b 4M c M 2

Figure shows a spherical body floating on liquid surface Line AB represents diameter of sphere Assume liquid and material of body makes a non wetting combination with contact angle 143 at the circumference of sphere passing through AB surface tension 0 05N density of liquid 4 x 103 kg m Density of sphere D x10 kg m radius of sphere 2 mm g 10m s Find D

2 2 Water from a tap emerges vertically downwards with an initial speed of 10 ms The cross sectional area of the tap is 104 m 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 10 ms 2 a 2x105m 2 c 5 104 m 2019 Main 10 April II 5 2 b 1x 10 m 5 2 d 5 x 10 m

7 Water is filled in a cylindrical container to a height of 3 m The ratio of the cross sectional area of the orifice and the beaker is 0 1 The square of the speed of the liquid coming out from the orifice is g 10m s 2005 2M 3 m 2 a 50m s 2 c 51m s 52 5 cm b 50 5m s d 52m s

1 The ratio 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 and 0 respectively It is observed that mercury gets depressed by an amount h in a capillary tube of radius while water rises by the same amount h in a capillary tube of radius 2 The ratio r n is 2019 Main 10 April 1 then close to a 3 5 b 2 3 c 2 5 d 4 5

A large tank is filled with water p 10 kg m A small hole is made in the side wall of tank at depth 10 m below water surface A water jet emerges horizontally from the hole and falls at a horizontal distance R from it What amount of extra pressure in atm must be applied on the water surface so that range becomes 2R on the ground Cross section area of hole is negligible 1 atm 105 Pa g 10 m s

range R an orifice is made at the depth of h from the upper surface of incompressible liquid If the height of liquid column in open vessel is 100 m then the value of his 100 m 1 10 m 3 50 m h R 2 20 m 4 70 m

A cube of density p is just balanced at interface of two unmixable liquid A and B having density p and P respectively as shown then the fraction of volume of cube in the upper liquid is p p P 1 3 P P P P P P P p 2 4 P P P P P P P

Mechanical Properties of Fluids 23 Equal volumes of two immiscible liquids of densities and 2p are filled in vessel as shown in figure Two p h 3h small holes are punched at depth 2 2 the surface of lighter fluid If v and v are the velocities of efflux at these two holes Then V V is 1 1 2 2 2 1 2 3 4 1 4 T 2p and from

8 10pts A bending operation is to be performed on 4 0 mm thick cold rolled steel sheet with tensile strength 350 MPa and shear strength 250 MPa The sheet is 25 mm wide The resulting sheet metal p is to have flange lengths of 40 mm and 50 mm an included angle of 30 and a bend radius of 6 mm Determine a the bend allowance and b the length of the starting blank