Fluids Questions and Answers

Two balls of same radius and weight are suspended on threads so that their surfaces are in contact A total charge of Q 4 x 10 7C is given to the balls makes them repel each other to an angle of 60 The angle of divergence becomes 54 when balls are immersed in kerosene Find the density s of the material of the balls if the distance from the point of suspension to the centre of the ball is 0 2 m Density of kerosene o 800 kg m dielectric constant k 2 tan 27 0 5

41 A bucket contains water filled upto a height 15 cm The bucket is tied to a rope which is passed over a frictionless light pulley and the other end of the rope is tied to a weight of mass which is half of that of the bucket water The water pressure above atmospheric pressure at the bottom is a 0 5 kPa c 5 kPa SIVIDE MVG b 1 kPa d None of these

55 A tube of radius r and sufficient height is dipped in a liquid of surface tension S and density p Heat developed upto steady state will be TS os 0 2 COS a pg 2 S cos 0 COS b d c pg 815 0 Note 9 is the contact angle TS os 0 2 COS 2pg 4 S cos 0 pg

Two cylindrical tanks of radii r and 2r with their bases at the same level contain a liquid of density p to heights H and 3H respectively as shown in figure The tanks are linked through a pipe of very small cross sectional area A Due to pressure difference liquid starts flowing from narrower vessel to broader vessel to equalize the pressure Based on above information answer the following questions The final common level of liquid in both vessel is 3H HI 2r

5 A helium balloon can just lift a load of 750 N The skin of the balloon has a mass of 1 40 kg What is the volume of the balloon the density of air is 1 29 kg m and the density of helium is 0 179 kg m m3

It is sufficiently long so that water rises to maximum height h in the tube The length of the portion immered in water The lower end of the tube is closed the tube is taken out and opened again Then 1000 x 4 8 008 4 MR 2006 8 11 B Q 1 all water flow out of the tube 2 the length of the water column remaining in the tube will be h 3 the length of the water column remaining in the tube will be 2h 4 the length of the water column remaining

4 A lead block is suspended by means of a string from the underside of a 6 50 kg block of wood of density of 688 kg m If the upper surface of the wood is just level with the water what is the mass of the lead block The density of lead is 11340 kg m kg

8 A plane is in level flight and each of its wings has an area 20 m If the speed of air on upper and lower surface are 80 m s and 70 m s respectively then the mass of plane is density of air 1kg m Oa 1500 kg O b 1700 kg O c 1650 kg d 1750 kg

A 5 99 6 m OT4 5 67x10 8 16 108 60 An air bubble in a water tank rises from the bottom to the top Which of the following statements are true a Bubble rises upwards because pressure at the bottom is less than that at the top b Bubble rises upwards because pressure at the bot tom is greater than that at the top c As the bubble rises its size decreases d As the bubble rises its size increases Explanation B H U 2008 Im b 2 898 This wavelength 64 The latent hea ways a Greater th b Greater th c Equal to i d Less than Explanation Ly L 65 The total ra direction o

14 A solid cylinder of mass m length 1 and radius r is rotating about its axis in a hollow cylinder of inner radius 2r filled with a liquid of coefficient of viscosity n The time in which angular speed becomes half is where a is mln2 a nl SECTION III COMPREHEN SIN TYPE This section contains 2 Paragraphs Based on each paragraph there are 2 questions Each question has 4 options A B C and D for its answer out of which ONLY ONE option can be correct Marking scheme 3 for correct answer 0 if not attempted and 1 in all other cases Paragraph for Question Nos 15 to 16 248 The element Curium Cn has a mean life of 10 3 seconds Its primary decay modes

Q 35 A brass bar having cross sectional area of 1000 mm subjected to a forces in figure below Find the stress induced in the portion BC in kN mm Take E 2 1x105 N mm 50 kN 600 mm B 80 KN 20 kN C D 10 kN

AU Tube contains two liquids in static equilibrium Water In right arm and oll of unknown density In left arm Measurement given are 136 mm and d 12 mm the density of oil is U oil interface O 919 kg m 3 O 712 kg m 3 O 629 kg m 810 kg m 3 water

A tank of area A is filled with two immiscible liquids of density 2p and p with height h and 2h respectively as shown in figure If a small orifice of area a is made near bottom the total time kA h 1 a g 2 required to empty the tank is the value of k is 2h 2

1 Oil is poured into the open side of an open tube manometer containing mercury What is the density of the oil if a column of mercury 5 00 cm high supports a column of oil 65 0 cm high The density of mercury is 13 600 kg m kg m

A U Tube contains two liquids in static equilibrium Water i right arm and oil of unknown density in left arm Measurement given are 136 mm and d 12 mm the density of oil is oil interface www 919 kg m 3 712 kg m 3 629 kg m 3 810 kg m water

Three cylinders A B and C are filled with gases at different pressures Two mercury manometers X and Y are connected to the three cylinders as shown in the figure When the right arm of the manometer X is disconnected from the cylinder B the level of the mercury in its left arm rises by 23 cm If the initial level of the mercury in the limbs of the manometers is 60 cm determine the pressure exerted by the gases in the cylinders A B and C atmospheric pressure 76 cm of Hg A common hydrometer has a long uniform stem When floating in pure water 4 5 cm of stem lies below the A 65 cm B 55 cm

1 An air bubble of small radius R is inside a liquid of surface tension T and density p If bubble is at a depth h below the free surface of liquid then absolute pressure inside the bubble is Po is atmospheric pressure 1 Po pgh 4T R 27 2 Po pgh 27 R 2T

A sphere of radius 10 cm and density 500 kg m is under water of density 1000 kg m The acceleration of the sphere is 9 80 m s upward Viscosity of water is 1 0 centipoise If g 9 81 m s the velocity of the sphere is Question Type Single Correct Type 1 2 10 m s 3 9 m s 4 11 m s 12 m s

A uniform vertical cylinder density a is released from rest when its lower end just touches the liquid density p surface of a deep lake Calculate maximum displacement of cylinder in meter Take t 8m and 1 P 2 AL

The capillary tube is dipped in water vertically It is sufficiently long so that water rises to maximum height h in the tube The length of the porti immered in water is t h The lower end of the tube is closed the tube is taken out and opened again Then all water flow out of the tube the length of the water column remaining in the tube will be h the length of the water column remaining in the tube will be 2h the length of the water column remaining in the tube will be h Marks 4 1

required ratio 32 A canister has a small hole at its bottom Water penetrates into the canister when its be at a depth of 40 cm from the surface of water if surface tension of water is 73 5 dynerce the radius of the hole As the water tries to enter the hole

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 ym anzi a gyere e te di ma 46 4 cm R 4 8 cm 9 2 3 3 81 3

Two soap bubbles of equal radii R 8cm are stuck together with an intermediate film separating them Surface tension of solution forming bubbles is 7x10 Newton meter What will be distance between the central of soap bubbles in cm

In a large rectangular water tank water is coming out of a small hole at the bottom of the tank It takes almost 4 min to empty half of the tank How much approximate further time will be needed to empty the tank completely 1 4 min 3 10 min 2 6 min 4 8 min

7 46 A level controller is shown in the figure 7 113 it consists of a thin circular plug of diameter 10 cm and a cylindrical plug of diameter 20 cm tied together with a light rigid rod of length 10 cm The plug fits in smoothly in a drain hole at the bottom of the tank which opens into atmosphere As water fills up and the level reaches height h the plug opens Find h Determine the level of water in the tank when the plug closes again The float has a mass 3 kg and the plug may be assumed as massless 2 3 h Float AHHH 10 cm Figure 7 113 Plug

In the figure shown density of lower liquid is three times of density of upper liquid The cross sectional areas of openings shown are same The ratio of mass flow rate from upper opening to lower opening at initial moment is A C 3 2 1 E B 3 D 2 3 P P2

A solid sphere of density n 1 times lighter than water is suspended in a water tank by a string tied to its base as shown in fig If the mass of the sphere is m then the tension in the string is given by 1 3 n l n mg n mg 2 mg 4 n 1 mg

Two glass plates of width b are kept close to each other in water at a small distance d as shown in figure Density of water is p surface tension T while contact angle with glass is 0 The force with which two plates attract each other A 2T b pgd C 27 d pgb B D 4T b pgd 4T d pgb

A solid has a volume vo when external pressure is po Bulk modulus of the material is B Now the pressure is increased to p The additional energy per unit volume now stored in the material is 3 p p Find z zB

Passage 3 Q Nos 8 to 10 A wooden cylinder of diameter 4r height h and density p 3 is kept on a hole of diameter 2r of tank filled with liquid of density p as shown in the figure Ini 4r p 3 a 4h 9 c 5h 13 P 2r 8 Now level of the liquid starts decreasing slowly When the level of liquid is at a height h above the cylinder the block starts moving up At what value of h will the block rise b 5h 9 d Remains same

Which one of the following cannot be explained on the basis of Bernoulli s theorem A Blowing off of light roofs when strong winds blow B Curved path followed by a spinning ball C Working of an atomizer D Rise of liquid through a capillary In the following figure is showing the flow of an ideal liquid through nnected to the CH

A cylindrical buoy of mass 942 4 kg has a diameter of 1 2 m and it is floating in salt water with a density of 1030 kg m3 A 76 6 kg man steps from a boat onto the buoy Determine the new depth of the buoy below water

If two glass plates have water between them and are separated by very small distance see figure it is very difficult to pull them apart It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by A C 27T R T 4R Cylindrical surface of water B D 47 R R

A block of wood of relative density 0 5 is placed 10 m inside a vessel containing water The vessel is accelerated upward with an acceleration of 10 m s If the block is released at some instant then the time taken by the block to reach the surface of water from that instant is consider g 10 m s A 0 5 s C 2 s B 1 s D 4 s

14 Figure shows a vessel of depth R having a pipe of small cross sectional area considered very small as compared to area of vessel in the shape of a circular arc of radius R as marked Identify the correct statement R B H A H R for all possible values of 0 between 0 to 45 B H R is possible for some angle 0 between 45 to 90 C Initial value of H for 0 60 is more than for 0 45 D H R is possible for atleast 2 different 0 between 0 to 90 A 4 8

of 1 3 A copper density of Cu P ball of diameter d is immersed e in oil of density p What is the charge on the ball if in a homogeneous electric field E directed vertically upward it is suspended in the oil k nd3 Pc8 il 2 k nd PcB E A 4 1 P Po 14 1 P 2 C B k 1 Po Pc Po 10 4 1 00 k

Two drops of same radius are falling through air with steady speed v If the two drops coalesce what would be the terminal speed A v B 2v C 3v D None

A conical flask of mass 10 kg and base area as 10 cm is floating in liquid of relative density 1 2 as shown in the figure The force that liquid exerts on curved surface of conical flask will be Given g 10 m s A 20 N downward direction B 40 N in downward direction C can be determined only if 0 is given D 20 N in upward direction 10

One end of a glass capillary tube with a radius r 0 005 cm is immersed into water to a depth of h 2 cm What pressure is required to blow an air bubble out of the lower end of the tube T 7 x 10 N m and p 10 kg m g 10 m s

The following data represents the relation between the dynamic viscosity of water and the temperature Temperature C 3 8 13 18 23 28 Dynamic viscosity of water u x 10 3 N s m 1 984 1 842 1 365 1 042 0 942 0 823 5 Predict the value of at a temperature of 20 C using the quadratic regression function 6 Using any type of interpolation find the 5th order polynomial which describes this relation then find the value of when the temperature is 20 C

7 35 In a given U tube open at one end and closed at other end as shown find out the correct relation between p and patm Given d 2 x 13 6 gm cm d 13 6 gm cm y 25 cm d Figure 7 90 P x 26 cm d

7 23 A block is partially immersed in a liquid and the vessel is accelerating upwards with an acceleration a The block is observed by two observers O and O one at rest and the other accelerating with an acceleration a upward The total buoyant force on the block is Figure 7 85 A same for O and 0 C greater for O than 0 0 of 1 of at rest B greater for O than O D data is not sufficient

ROTATRA Between two parallel long wires AB and CD is a wires PQ EF The separation between PQ EF is x which can be statement s is are 08 C S E B end a nolo Q F D A Force due to surface tension on PQ equals in magnitude to that on EF B Force of surface tension is proportional to the separation x Force of surface tension is proportional to length of PQ and EF 20

7 19 The manometer shown below is used to measure the difference in water level between the two tanks Calculate this difference for the conditions indicated Water A 2 cm C 6 cm 40 cm Figure 7 83 Liquid specific gravity 0 9 Pa 4 cm D 8 cm Water 292

7 24 A person can change the volume of his body by taking air into his lungs The amount of change can be determined by weighing the person under water Suppose that under water a person weighs 20 0 N with partially full lungs and 40 0 N with empty lungs Find the change in body volume Ans 2 04 10 m

35 What force must be applied to detach two wetted photographic plates 9 cm x 12 cm in size from each other without shifting them The thickness of water between the plates is 0 05 mm Surface tension of water is 0 073 N m a 31 5 N c 40 5 N b 16 5 N d 20 0 N

Example 13 27 Two spherical raindrops of equal size are falling vertically through air with a terminal velocity of 1 ms What would be the terminal speed if these two drops were to coalesce to form a large spherical drop 1

7 6 Water from a tap emerges vertically downwards with an initial speed of 1 m s The cross sectional area of the tap is 10 m Assume that the pressure is constant throughout the stream of water and that the flow is steady Find the cross sectional area of the stream 0 15 m below the tap Ans 5 x 10 5 m

COMPREHENSION A tank has a hole of area 2 cm at its bottom and in this hole a conical cork and water is filled up The water level is made to fall slowly by means of another orifice in the tank When the water level comes to a height of H cm the conical cork mass of the cork 40 gm Area of hole 2 cm density of water 1 gm cm Area of just comes out from the hole Given volume of water displaced by the cork 80 cm circular cross section of conical cork 8 cm Height of cork submerged in and P 105 N m 120 22 water cm Take g 10 m s 7 7 38 Calculate the value of H A 15 cm C 22 cm 39 B 20 cm D 17 cm A 1 3 N C 0 63 N Calculate the force exerted by water on the curved surface of the conical cork submerged water when the liquid level in the vessel is equal to H B 60 63 N D 70 63 N H The total force exerted by all the fluids on the conical cork in the vertical direction is A 0 4 N B 0 8 N C 1 N D 1 4 N

Consider a cuboidal vessel 2R x 2R x R with a hemispherical cavity of radius R kept at a horizontal smooth surface as shown in the figure The vessel has very small hole of cross sectional area a Now water of density p is poured into space developed due horizontal surface and vessel through hole very slowly When the height of water level is h the vessel lifts off the surface and liquid leaks through space generated R 2m p 10 kg m m 9 kg If the value of h is 5k cm find the valve of k Atmospheric pressure 105 N m