Fluids Questions and Answers

7 A glass flask with volume 200 cm is filled to the brim with mercury at 20 C How much mercury overflows when the temperature of the system is raised to 100 C The coefficient of linear expansion of the glass is 0 40 x 10 5 K 1 Cubical expansion of mercury 18 x 10 5 K 1 The

Soap solution can be spread into a fairly large vertical thin film but the same cannot be done with water Why A Density of water is more than that of soap solution B Surface tension of water is more than that of soap solution C Surface tension of water is less than that of soap solution D Because of some reason other than those

13 There are two holes each of cross sectional area a on the opposite side of a wide rectangular tank containing a liquid of density p When the liquid flows out of the holes the net force on the tank is h vertical distance between the two holes S2apgh 2 4apgh 4 apgh 3 0 5apgh

are Two immiscible filled in a vessel The velocity with which the liquid will emerge out of a narrow hole at the bottom is 6gH 4gH 21 2H PA 0 5 g cc HP 1 0 g cc

4 A glass rod of radius 1 mm is inserted symmetrically into a glass capillary tube with inside radius 2 mm Then the whole arrangement is brought in contact of surface of water Surface tension of water is 7 x 10 2 N m To what height will water rise in capillary 1 0 93 cm 2 1 4 cm 3 2 1 cm 4 6 8 cm

8 A Liquid in a cylindrical vessel of radius 0 05 meter is rotated along with the vessel about its axis with a speed of 4 radian sec The rise in liquid level will be g 10 m sec 1 0 002 M 2 0 01 M 3 0 2 M 4 0 1 M 8

Q 9 One cubic plate having 15 cm side floats on water surface If surface tension of water is 60 dyne cm To lift this plate from water Find the extra force required against weight 1 3600 dyne 2 1800 dyne 3 900 dyne 4 7200 dyne

A power P is required in maintaining the liquid flow through a pipe at velocity v If the speed of flow is doubled the new power required will be 1 8P 2 4P 3 2P 4 P 100 5

7 42 A tank is filled with a liquid upto a height H A small hole is made at the bottom of this tank Let t be the time taken to empty first half of the tank and t the time taken to empty rest 4 half of the tank Then find 1

The small piston of a hydraulic lift has a cross sectional area of 3 cm and its large piston has a cross sectional area of 200 cm What force must be applied to the small piston to lift a load of 12 0 kN Select one O a 1 80 N b 18 0 N c 180 N

A liquid flows through two horizontal sections of tubing joined end to end In the first section the cross sectional area is 12 0 cm the flow speed is 250 cm s In the second section the cross sectional area is 2 50 cm Calculate the flow speed of the smaller section Select one O O a 12 cm s b 1200 cm s c 120 cm s

Light rays from a very small object im water falls on the bubble of radius R Assume tha the object is very close to the surface of the 4 bubble Refractive index of water is 3 Take the approximation sine 0 and cose 1 where 0 is angle and consider the rays close to a diameter of the bubble Use the following formula to solve the problem sina sin sin y a b C XELL C Object a a see figure R b The image is from the center of the bubble Y Jame Air bubble Water 1 Virtual and formed at a distance 3R 2 2 Virtual and formed at a distance 3 Virtual and formed at a distance 2R 3 3R 5

that is 50 mm thick Use shear strength as 350 MN m and 22 7 A horizontal pipe has a cross section of 10 cm in one region and of 5 cm in another Th water velocity at the first is 5 ms and the pressure in the second is 2 x 105 Nm 2 Th pressure of water in 1st region is given by 237 5 x 10 Pa Then the value of a is

A liquid of density p flows along a horizontal pipe of uniform cross section A with a velocity v through a right angled bend as shown in Fig What force has to be exerted at the bend to hold the pipe in equilibrium V 45 V

A spinning ball is moving in a direction opposite to the direction of the wind The ball moves in a curved path as a the pressure at the top and the bottom of the ball are equal b the pressure at the top the pressure at the bottom c the pressure at the top the pressure at the bottom d there is no relation between the pressures

2 A vertical U tube of uniform cross section contains water in both the arms A 10 cm glycerine column R D 1 2 is added to one of the limbs The level difference between the two free surfaces in the two limbs will be A 4 cm B 2 cm

As the atmospheric pressure decreases A The spring become more compressed B The spring become less compressed The spring will be elongated D There won t be any change in the elongation of spring 1 20

nswer given a 5 Bottom arm of a U tube of uniform section has length I and the vertica arms have length 31 each The tube is held with its parallel arms vertica and filled with a liquid of density p to occupy a total length of 4l of the tube and then it is made to accelerate horizontally in the plane of the tube with an acceleration g that is modulus of acceleration of free fall What will gauge pressure at the midpoint of the bottom arm b immediately after acceleration of the tube is made abruptly zero a pgl c 50gl b 2 pgl d 1 375 ogl

Fig 2 2 shows the same measuring cylinder after stone A has been lowered into it on a fine tring f 12 Fig 2 1 44 2 cm water Calculate the volume of stone A Fig 2 2 60 4 cm volume b The mass of stone A is measured as 40 5g Calculate the density of the rock from which stone A was formed cm 2

A vessel of volume V and thermal coefficient of linear expansion a is completely filled with a liquid The liquid does not overflow on heating The thermal coefficient of volume expansion of liquid is 1 V a V 3 G 2 V V a 4 3 a

A stone is tossed into a pond creating a circular ripple The radius of the ripple increases by 12 cm s a Write an equation that describes the ripple exactly 3 s after the stone lands in the water Use the origin as the point where the stone lands in the water b A bulrush is located at point 36 48 When will the ripple reach the bulrush

A block of wood floats in freshwater with two third of its volume submerged In oil the block floats with one fourth of its volume submerged The density of oil is A 2666 7 kg m C B 5333 3 kg m 3 1333 3 kg m 3 D 3 Correct Answer 3333 3 kg m 3

C 15 A bucket has oil of density 1 2 g c c upto a height of 3 cm On top of the oil is a water column of height 10 cm If density of mercury is 13 6 g c c the pressure at the bottom of the beaker due to liquids is C P M T 1993 1 1 cm of mercury 2 5 cm of mercury 3 13 cm of mercury 4 15 cm of mercury

A glass rod of diameter d 1 5 mm is inserted symmetrically into a glass capillary with inside diameter d 2 0 mm Then the whole arrangement is vertically oriented and brought in contact with water To what height in cm will the water rise in the capillary Given surface tension of water 75mN density of water 10 kg m g 10 m s

A cork is suspended from the bottom of a container filled with water with a string as shown in figure The container accelerates in a horizontal direction towards right Then the inclination of the string with vertical is a tan a g towards left b tan a g towards right c cot a g towards left d cot a g towards right

n ice cube is floating in water above which a layer of lighter oil is poured As t e melts interface and the uppermost level of oil will respectively AT FIN 111 Ice rise and fall not change and not change HAN MIT Interface 2 fall and rise 4 no change and fall

A small sphere having radius R and made up of material of density p falls from rest vertically from a height h into a liquid of density 3p The period of oscillation is O O 2 2h 9 2h 9 O 2h 9 3h 9

Consider a syringe of diameter 10 mm and a needle of diameter 1 mm attached to it In order to administer the Corona virus vaccine a nurse is pushing the piston in the syringe keeping it horizontal If the vaccine is having a velocity of 10 mm s inside the syringe then find the force applied by the nurse on the piston Take density of vaccine as 1 gm cm and assume that the needle releases the vaccine to atmospheric pressure O 0 039N O 1 2N O 0 156N O 0 078N

diameter 1 mm attached to it In order to administer the Corona virus vaccine a nurse is pushing the piston in the syringe keeping it horizontal If the vaccine is having a velocity of 10 mm s inside the syringe then find the force applied by the nurse on the piston Take density of vaccine as 1 gm cm and assume that the needle releases the vaccine to atmospheric pressure O O 0 039N 0 156N

18 The velocity of viscous fluid in contact with surface is 1 Same as that of the surface 2 More than that of the surface 3 Less than that of the surface 4 Always zero

Capillary tube with very thin walls is suspended vertically in a cup containing water Before the capillary is suspended the cup was balanced against weights on a beam balance When capillary is dipped to a small distance in the water water rises in the capillary Water completely wets the capillary walls To restore the balance we have to decrease the load on the other scales by 0 14 g If the surface tension of water is 0 07 N m determine the radius r in mm of the capillary

The Gardener water the plants by a pipe of diameter 1 mm The water comes out at the rate of 10 cm sec The reactionary force exerted on the hand of the Gardener is density of water is 10 kg m A B 1 27 x 10 N U zero O 1 27 x 10 4 N 0 127 N X

As shown in the figure water of density 1000kg m is flowing steadily in a pipe of non uniform cross sectional area The area at wider section is 0 2m and the area at the narrower section is 0 1m The pipe lies in the horizontal plane The speed of liquid at point P is 2m s Determine the difference in pressures at P and Q A B C 4000 Pa 5000 Pa 6000 Pa k

9 A wooden plank is floating on water in a pool It is tethered to the botte of the pool by a string attached at mid point of an edge of its bottom fa which causes it to float with a diagonal of one of its vertical cross secti coinciding with the level surface of the water as shown in the figu What is the specific gravity of the wood a 1 5 c 1 3 b 1 4 d 1 2

Water is filled in a uniform container of area of cross section A A hole of cross sectional area a A Is made in container at a height of 20m above the base Water stream out and hits a small block placed at some distance from container with what speed in m s the block should be moved such that water streams 1 take g 10m s A 20 always hits the block Given

A lawn sprinkler has 20 holes each of cross sectional area 2 x 10 2 cm and is connected to hose pipe of cross sectional area 2 4 cm If speed of water in hose pipe is 1 5 ms speed of water as it emerges from holes is 6 ms 1 9 ms 1 12 ms 1 15 ms 1

A vertical U tube of uniform cross section contains mercury in both of its arms A glycerine p 1 3 g cm column of length 10 cm is introduced into one of the arms Oil of density 0 8 g cm is poured into other arm until the upper surfaces of oil and glycerine are in same horizontal level What is length of oil column PHg 13 6 g cm U 10 cm Glycerine Mercury 0 96 cm 1 2 cm 4 8 cm 9 6 cm oil x

A 90 kg bicyclist is coasting down a long hill that has a 10 slope His cross section area is 0 35 m his drag coefficient is 0 85 his bicycle s coefficient of rolling friction is 0 02 and the air temperature is 20 C Part A What speed does he eventually reach Express your answer with the appropriate units D

m upwards 8 A ball is suspended with the help of two threads inside an empty cylindrical vessel without touching its walls from two points on the walls of the vessel If the vessel is filled with water up to such a height that the ball remains submerged and both the threads become taut tension forces in the threads remain the same as they were in the empty vessel Density of water is 1000 kg m Which of the following is a correct statement a Density of the ball is 500 kg m if threads are of equal length b Density of the ball is 500 kg m if the threads are of equal length and affixed on walls of the vessel at equal heights c Density of the ball is 500 kg m if the threads are of equal length and affixed on walls of the vessel at equal heights on diametrically opposite points d Density of the ball is 500 kg m irrespective of lengths of the threads and location of point of suspension

iii On the opposite sides of a wide vertical vessel filled with water two identical holes are opened each having cross sectional area S The height difference between them is equal to Ah Find the resultant force of reaction of the water flowing out of the vessel F 2 Ah p g S

resistance becomes times 16th Page 3 Reason In parallel net resistance is less than the smallest value of individual resistance a Assertion and Reason both true and Reason is correct explain of assertion b Both assertion and reason true but reason not correct explanation of assertion

Assertion Half of the ring is uniformly positively charged and another half uniformly negative charged then electric field and electric potential both zero at centre Reason At the centre of uniformly charged ring electric field is zero a Assertion and Reason both true and Reason is correct explain of assertion b Both assertion and reason true but reason not correct explanation of assertion c Assertion is false but reason true d Assertion true but reason false

Figure shows a U tube of uniform cross sectional area A accelerated with acceleration a as shown If d is the separation between the limbs then the difference in levels of the liquid in the U tube is hi h Pro

7 27 A J tube shown in figure 7 106 contains a volume V of dry air trapped in arm A of the tube The atmospheric pressure is H cm of mercury When more mercury is poured in arm B the volume of the enclosed air and its pressure changes Wha should be the difference in mercury levels in the two arms so a to reduce the volume of air to 1 2 A air volume v Figure 7 106 B Hg

An iceberg is floating in water The density of ice in the iceberg is 917 kg m 3 and the density of water is 1024 kg m 3 What percentage fraction of the iceberg would be visible 1 5 3 12 2 10 4 8

A capillary tube A is dipped in water Another identical tube B is dipped in a soap water solution Which of the following shows the relative nature of the liquid columns in the two tubes Question Type Single Correct Type 1 2 3 B B B

A long cylindrical tank of cross sectional area S is filled with two immiscible liquids of densities pand 2p It has two holes of cross section S 10 one is just abov liquid interface hole B another one at the bottom hole A as shown in figure A light movable piston frictionless of cross sectional area almost equal to S is fitted on the top of the tank A load of mass M is kept on the piston Match the responses in List Il with corresponding statements in List I M Hole B Hole A List 1 P Initial speed of water jet at hole A Oinitial speed of water jet at hole B 1 2 R Maximum force exerted by water jet of hole A on the tank 3 5 Maximum force exerted by water jet of hole B on the tank 4 List II 3gll p Mg 3pSHg 5 2Mg V ps Mg pSHg 5

Water flowing from one Tube to another Water is flowing through two horizontal pipes of different cross sections which are connected together In first pipe the speed of water is 4 m s and the pressure is 2 x 104 N m Calculate the speed and pressure in second pipe The diameters of the pipes are 3 cm and 6 cm respectively

A cuboidal container has dimension 50 cm X 30 cm X 100 cm it is completely filled with water having density 10 kg m Find pressure at the depth of 25 cm from the surface of the vessel if the atmospheric pressure is 10 N m 4

36 Water is flowing through a horizontal tube having cross sectional areas of its two ends being A and A such that the ratio 4 4 is 5 If the pressure difference of water between the two ends is 3 105 N m 2 the velocity of water with which it enters the tube will be neglect gravity effects a 5ms b 10ms 1 2019 c 25 ms 5010 ms