Fluids Questions and Answers

5 A container holds two immiscible ideal fluids of as shown in H density d and 2d each of height 2 figure The height h as shown in figure at which hole should be punched so range of liquid is maximum IN IN 1 3 IN Ile wwwww 2d 3 3 3 h 2 3 4 R H4 30 8 H

with a liquid up to height H as shown in figure There are two holes in the container such that water coming out from them have same range If the range of water coming out of the holes is equal to 2 H Then the distance X between the holes is 1 3 7 2 H 7 H R 3H 4 2 4 7 F L 3H 2

Water flows in a horizontal tube as shown in figure The pressure of water changes by 600 N m between x and y where the areas of cross section are 3cm and 1 5cm2 respectively Find the rate of flow of water through the tube X

19 The weight of a body in water is one third of its weight in air The density of the body is 1 0 5 g cm 2 1 5 g cm 3 2 5 g cm 4 3 5 g cm

28 A straw 6cm long floats on water The wate film on one side has surface tension of dyne cm on the other side camphor reduc the surface tension to 40 dyne cm T resultant force acting on the straw is 1 60 dyne 2 10 dyne 3 30 dyne 4 0 dyne

d 6 8 A block of wood with a metal plate placed on its top floats in water as shown in figure with x 2 cm and y 50 cm the possible value of x and y after metal plate has fallen in water Metal sink level in lig falls less lepthrust Vo muse 1 3 cm 52 cm 3 1 cm 51 cm Metal plate Wood 2 3 cm 49 cm 4 1 cm 18

3 A piece of wood is floating in water When the temperature of water rises the apparent weight of the wood will 1 Increase 2 Decrease 3 May increase or decrease

Two circular plates of radius 5 cm each have a 0 01 mm thick water film between them Then what will be the force required to separate these plate S T of water 73 dyne cm a 125 N b 95N c 115N d 105 N

1 3 T 33 Pressure inside two soap bubbles are 1 02 atm and 1 05 atm respectively The ratio of their surface area is 125 25 4 2 3 5 2 2 5 Road New Delhi 110005 Ph 011 4782345

Two spheres of volume 250 cc each but of relative densities 0 8 and 1 2 are connected by a string and the combination is immerssed in a liquid The tension in the string is g 10 m s 1 5 0 N 2 0 5 N 3 1 0 N 4 2 0 N

A liquid of density d is pumped by a pump P from situation i to situation ii as shown in the diagram If cross section of each of the vessel is a then the work done in pumping neglecting friction effects is A dgh a C dgha h B 2 dgh D 2 dgh a P 2h

A tank is filled upto a height n placed on a platform of height h fromt he ground To get maximum range x a small hole is punched at a distance of y from the free surface of the liquid m Then KEL T h 1 x 3h m 3 y h y X m 2 x 1 5h m 4 y 0 75 h

A small ball of density 4p0 is left from the surface of liquid The density of liquid varies as p Po 1 ay where y is height of liquid from the surface and po a are 2 constants The time period of oscillation of ball is found to be K g 10ms 1 Neglect viscosityl 1 K a 2 m sec Find

An open U tube contains mercury When 13 6 cm of water is poured into one of the arms of the tube then the mercury rise in the other arm from its initial level is 1 1 cm 2 0 5 cm 3 10 cm 4 5 cm

SO An empty plastic box of mass m is found to accelerate up at the rate of g 6 when placed deep inside water How much sand should be put inside the box so that it may accelerate down at the rate of g 6

B Water and oil are poured into the two limbs of a U tube containing mercury The interfaces of the mercury and the liquids are at the same height in both limbs Determine the height of the water column h if that of the oil h 20 cm The density of the oil is 0 9

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury If the density of mercury be 13 6 10 kg m and g 10m s then the power of heart in watt is 1 1 50 2 1 70 3 2 35 4 3 0

29 A liquid drop of mass m and radius ris falling from great height Its velocity is proportional to 2 7 7 177

Continent density 2800 kg m Mantle rock density 3300 kg m Problem 5 The figure above on the left shows an iron ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water The cylinder has a height of 0 06 m a face area of 0 0012 m on the top and bottom a density of 300 kg m and 0 04 m of its height is below the wa ter surface What is the volume of the iron ball The density of iron is 7900 kg m Answer 38x10m

1 2 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 3 T 4R T 2R 4T R 2T E Cylindrical surface of water

29 A light cylindrical vessel is kept on a horizontal surface Its base area is A A hole of cross A sectional area is made on side wall just at its 4 bottom Minimum coefficient of friction such that it does not slide due to impact force of emerging liquid is 1 1 4 2 4 3 4 IN c 1 2 1

A large cylindrical container with open top contains a liquid upto height 2H 8m and whose density varies as shown in the figure Atmospheric pressure is 1 atm 10 N m Find the pressure at bottom of cylindrical container in atm given P 10 Kg m and g 10m s A

A tank of cross sectional area A is filled with a liquid A small orifice of area A A A is pesent at the bottom of the tank At a moment the height of liquid in the tank is H The acceleration of top layer of liquid at this moment is 1 g 3 A g 2 A A g 4 Depends on H

2 A motor of power P is used to deliver water at a certain speed through a given horizontal pipe To increase the speed of water through the same pipe three times the power of the motor is increased to P Then the ratio of P to P is 1 27 1 3 12 3 2 9 1 4 3 1

3 Goes out in a straight line 4 A concrete sphere of radius R has a cavity of radius r which is packed with of concrete and sawdust are respectively 2 4 and 0 3 for this sphere to float with its entire volume submerged under water The ratio of mass of concrete to mass of sawdust will be 3 3 2 4 1 8 4 Zero 5 A wire elongates by I mn when a load W is hung from it If the wire goes over longation of the wire will be in mm a pulley and two weights 1 21

The thrust acting on the base of vessel filled with water is take g A 10 N B 1 5 x 104 N C 2 104 N D 3 x 104 N 1m 10 m s area 2m p 10 Kgm area 1m

5 A barometer correctly reads the atmospheric pressure 76 cm of mercury Water droplets are slowly introduced into the barometer tube by a dropper The height of the mercury column first decreases and then

A container is filled with liquid upto height H as shown in figure There are 2 holes in the container such that water coming out from them have same range If the range of water coming out of the holes is half of maximum range then the distance x between these holes is 1 H 5H 4 2 3H 4 BH

A steel wire having cross sectional area 1 2 mm is stretched by a force of 120 N If a lateral strain of 1 455 mm is produced in the wire calculate the Poisson s ratio

9 Liquid is filled in a container Find the value acceleration a for which point x is exposed to as shown in the figure 1 3g L L X 2 4g 3 a

If the velocity of water layers in river is given by v ky where y is the height from the river bed The force required to keep a square plate of area A with constant velocity at height his n coefficient of viscosity Y A 1 nak MAK NAPA 2 4 Akh X

force of 1 N is required to move a metal plate of area 10 2 m with a velocity of 2 x 10 2 m s when it rests on a layer of oil 1 5 x 10 m thick Find the coefficient of viscosity of oil

Water flows through a pipe bent at an angle a to the horizontal with a velocity v What is the force exerted by water on the bend of the pipe of area of cross sectin S 2 2pv S cosa a 1 2pv S sin 2

reache 1 2H g 2 H g 3 2H 3g When a hole is made in the side of a container holding water water flows out and follows a parabolic trajectory If a hole is made in the side of the container and the container is dropped in free fall just before the water starts coming out the water flow neglect effect of surface tension

flow If pressure diffe through a single capillary of length L and radius R R is X Now two capillaries of length L 8nl and 2 L and radius R and 2R respectively are connected in series and same pressure difference is applied then rate of flow will be 8 1 X 2 X 8 3 X 4 X X

electron goes past the coil The cylindrical tube of a spray pump has radius R one end of which has n fine holes each of radius r If the speed of the liquid in the tube is V the speed of the ejection of the liquid through the holes is VR 1 V R 2 3 VR 4 VR

A wooden cube just floats inside water with a 200 gm mass placed on it When the mass is emoved the cube floats with its top surface 2 cm bove the water level What is the side of the cube 6 cm 10 cm 2 8 cm 4 12 cm

A gardener waters the plants by a pipe of diameter 1mm The water comes out at the rate of 10 cc sec The reaction force exerted on the hand of the gardener will be 1 zero 3 1 27 x 10 4 N 2 1 27 10 2 N X 4 0 12 N

A large open tank has two small holes in the wall One is 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 holes are the 2000 same Then R is equal to A L 2 T C L B 2 L D L 2T

A spherical body is thrown in a long column of viscous liquid with speed greater than terminal speed VT The correct variation of the speed v with time t is 1 3 VA VT O 2 VA VT O VA VT t

6 The bottom of a cylindrical vessel has a circular hole of radius r at depth h below the water level in it If diameter of the vessel is D then the speed with which the water level in the vessel drops is 1 3 x 2gh x 32gh 2 4 3r D x 2gh x 8gh

Water flows in a streamlined manner through a capillary tube of radius a the pressure difference being p and the rate of flow Q If the radius is reduced to a 2 and the pressure increased to 2p the rate of flow becomes 1 4Q 2 Q 3 4 olx

A meter long narrow bore held horizontally Closed at one end contains 76 cm long mercury thread which traps 15 cm column of air The length of air column becomes if the tube is held vertically wit open end at the bottom assuming temperature constant 1 18 cm 2 20 cm 3 24 cm 4 32 cm

44 A cylindrical tank having cross sectional area A is filled with water to a height of 2 0 m A circular hole of cross sectional area a is opened at the bottom If a A the velocity with which water emerges from the hole is g 10 ms 2 1 10 m s 3 5 0 ms 4 20 m s corries a constant L The velocity of free electrons drifting at a distance 2 15 m s

A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R The volume of the remaining cylinder is V and its mass is M It is suspended by a string in a liquid of density p where it stays vertical The upper surface of the cylinder is at a depth h below the liquid surface The force on the bottom of the cylinder by the liquid is A Mg C Mg R hpg B Mg V pg D pg V R h 2R O

Comprehension Q 3 to Q 5 gh fight The horizontal portion of a U shaped tube of small cross section sectional area 0 5 cm has a length 40 cm In the left vertical limb a liquid of density 2 g c c and volume 20 c c is poured while in the right limb a liquid of density 3 g c c and volume 25 c c is poured The top ends of the two vertical limbs are open to the atmosphere Find the difference in the heights of the liquid levels at equilibrium A 12 cm B 10 cm C 14 cm D 16 cm With what acceleration must the whole system be accelerated horizontally to the left so that the liquid levels in the two limbs become same 3 4 5 A 2g 17 B A 2 sec 23 6 4g 29 O B 2 sec 23 100 7g 29 2 C 2 23 500 CAROSM The U tube is now held fixed in a vertical plane and the liquid in the left limb is depressed by a small distance x Find the time period of subsequent oscillations of the entire liquid column sec 9 2 v 20 D 21 uom ha D None of these

4 Water leaks out from an open tank through a hole of area 2 mm in the bottom Suppose water is filled up to a height of 80 cm and the area of cross section of the tank is 0 4 m2 The pressure at the open surface and at the hole are equal to the atmospheric pressure Neglect the small velocity of the water near the open surface in the tank a Find the initial speed of water coming out of the hole b Find the speed of water coming out when half of water has leaked out c Find the volume of water leaked out during a time interval dt after the height remained is h Thus find the decrease in height dh in terms of h and dt d From the result of part c find the time required for half of the water to leak out

times that in B The ratio of the liquid thrust at the base of A to that at the base of B is Two vessels A and B have the same base area and contain water to the same height but the mass of water in A is four 1 4 1 2 2 1 A B 3 1 1 4 16 1 gob

A piece of zinc weighs 42g in air and 37 8g when immersed in oil having R D of 0 7 The R D of zinc is a 7 b 3 5 c 1 7 d 5 2

5 A normal force of 200 N acts on an area of 0 02 m Find the pressure in pascal Ans 10 000 Pa