Fluids Questions and Answers

20 cm column of air is trapped by a column of Hg 15 cm long in a capillary tube of uniform bore when the tube is held horizontally in a room where the atmospheric pressure is 75 cm of mercury The length of the air column when the tube is held vertically with open end up will be Trapped air Mercury column 20 cm 1 20 cm 2 25 cm 3 16 7 cm 4 18 9 cm 15 cm 270 cm 15 143 x 5 715 143 143 bisferio 143 810 143

0 A large fluid star oscillates in shape under the influence of its own gravitational field Using dimensional analysis find the expression for period of oscillation T in terms of radius of star R mean density of fluid p and universal gravitational constant G

1 Show that Equilibrium of a body on a rough inclined plane under any force theorem case i the body is about to move down along the inclined plane case ii the body is about to move along the inclined plane 2 write three Limitations of Archimedes Principle

A sphere of mass m and radius r rests at the bottom of a large reservoir of water as shown in figure I Depth of the reservoir is h Density of material of the sphere is the same as that of water Now the sphere is slowly pulled completely out of water as shown in figure II Which of the following is a correct expression for work done by the agent pulling the sphere a mgr c mg r h b 0 5mgr d mg 0 5r h Figure I Figure II

Let s assume you are performing the Archimedes lab s first part and trying to calculate the buoyant force of an object by using a graduated cylinder If the volume of water is 29 2 mL initially and 41 3 mL after you placed your metal piece in the graduated cylinder According to this data the buoyant force would be N Assume the density of water is 1000 kg m3 Please submit your answer correct to 2 decimal place

Q 8 Moderate O Apgh 4 1 A triangular lamina of area A and heigh h is immersed in a liquid of density p in vertical plane with its base on the surfa of the liquid The thrust on the lamina is 1 Apgh 00 18 O

A wind with speed 40 ms blows parallel to the roof that the pressure inside the house is atmospheric pressure the force exerted by the wind on the roof and the direction of the force will be pair 1 2 kgm3 roof area 250 m 1 2 4 x 105 N downwards 2 4 8 x 105 N downwards 3 4 8 105 N upwards 4 2 4 x 105 N upwards

At a given place where acceleration due to gravity is qms a sphere of lead of densityd k qm is gently released in a column of liquid of density pkqm If d p the sphere will Fall vertically with an acceleration Fall vertically with no acceleration

A boat carrying a number of large stones is floating in a water tank What would happen to the water level if a few stones are unloaded into water O Rises O Falls O Remains unchanged O Rises till half the number of stones are unloaded and the begins to fall

A cube of side length I is floating in a liquid i f density 1400 kg m 3 with half of the volu me inside the liquid Another liquid of densi ty 1000kg m 3 is poured gently in the beake r Then density of cube is Please answer f ast Please

O Calculate the rise of water inside a clean glass capillary tube of radius 0 1 mm whe immersed in water of surface tension 7 x 10 2 N m The angle of contact between water and glass is zero density of water is 1000 kg m g 9 8 m s Ans h 0 1428 m

5 A u tube is made up of capillaries of bore 1 mm and 2 mm respectively The tube is held vertically and partially filled with a liquid of surface tension 49 dyne cm and zero angle of contact Calculate the density of liquid if the difference in the levels o the meniscus is 1 25 cm take g 980 cm s Ans density of liquid 0 8 g cm

12 What are the relative humidity and dew point temperature of 1 kilogram of 25 Celcius air that contains 10 grams of water vapor Relative Humidity Dew Point Temp Celcius 13 If you wake up to a foggy morning what is the relative humidity NOTE Input your percentage as a percentage value not as a decimal value Ex type 55 if you mean 55 do not type 0 55

Consider the bottom of the cubic tank of edge x as reference level determine the gravitational potential energy of water completely filled in the tank Take the density of water as p and acceleration due to gravity as g A pgx4 B C 1 Pgx4 1 2Pgx4

The diagram shows a stone suspended on a string under the surface of a liquid The stone experiences a pressure caused by the liquid string liquid What would increase the pressure on the stone O A decreasing the surface area of the stone OC lowering the stone deeper into the liquid OB increasing the mass of the stone OD using a liquid with a lower density stone

7 A solid sphere of mass m is suspended through a string in a liquid as shown The string has some tension Magnitudes of net force due to liquid on upper hemi sphere and that on lower hemisphere are F and F respectively Which of the fol lowings is are true a Density of material of the sphere is greater than density of liquid b Difference of F and F is dependent on atmospheric pressure c F F mg d F F mg There are three wires MO NO and PQ Wires MO NO are fixed and

Water flows at 0 65 m s from a hot water heater through a 250 kPa pressure regulator The pressure in the pipe supplying an upstairs bathtab 2 5 m above the hater is 310 kPa What s the speed in this pipe

nk as ngure It s cross sectional area is 0 4 m The tank has an opening B near the bottom whose cross section area is 1 cm A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom the velocity of water coming out the opening B is v ms The value of v to the nearest integer is Take value of g to be 10 ms 24kg A 0

n E 800 kg m and side length l 50 cm is floating in a A cubical block of wood density rectangular tank partially filled with water density 1000 kg m Work done to press the block slowly so that it is just immersed in water is W Joules Area of the bottom of tank is 10000 cm take g 10 m s Find the value of W

The frequency of sonometer wire is f but when the weight producing the tension is completely immersed in water the frequency becomes and on immersing the weight in a certain liquid the frequency 3 becomes The specific gravity of the liquid is 4 O 15 16 O 128 O 135 128

A small orifice or area a is at the bottom of a tube or cross sectional area 3a Water filled up to height H in it and orifice is opened Acceleration of surface of water when water level falls to height H 4 is O 96 3g

A nozzle receives 0 1 kg s steam at 1 MPa 400 C with negligible velocity The exit is at 500 kPa 350 C and the flow is adiabatic Find the nozzle exit velocity and the exit area u 438 7 m s A 1 3 cm A diffuser has air entering at 100 kPa 300 K with a velocity of 200 m s The inlet cross sectional area of the diffuser is 100 mm At the exit the area is 860 mm and the exit velocity is 20 m s Determine the exit pressure and temperature of the air P 123 92 kPa T 319 74 K

A hollow thin hemisphere of mass M and radius R lies on a flat horizontal rubber surface In the upper hemisphere there is a small hole in which a long thin tube is inserted Fig Hemisphere tube is filled with water To what maximum height can be poured the water into the tube M 2 TR P

A cubical wooden block has side a 30 cm It is floating a rectangular tank partially filled with water and having ba area A 45 cm x 60 cm Calculate the work done to press block slowly so that it is just immersed in water 3 3 Pblock 500kg m Pwater 1000 kg m

6 Figure shows a capillary tube of radius r dipped into water If the atmospheric pressure is P the pressure at point A is S is surface tension of liqued A Po B P A H 2S r C P 2S r D P 4S

c move in same direction d move with same speed 14 If the kinetic energy of the particle is increased to 16 times its previous value the percentage change in the de Broglie wavelength of the particle is CBSE AIPMT 2014 d 50 a 25 b 75 c 60 15 What is the de Broglie wavelength of the electron accelerated through a potential difference of 100 V KCET 2014

A wooden block of mass 8 kg is tied to a string attached to the bottom of a tank The block is completely inside the water The tension in string is Relative density of wood is 0 8 and g 10 m s 1 100 N 280 N 3 50 N 4 20 N n

A body of dimensions 2 7x3 8x2 5m is completely submerged in water weighs 2500 N in water Find its weight in air 254 12 kN 508 25 KN

Surface tension o 490 10 Nm 1 1 03 mm 2 1 53 mm 3 1 03 cm 4 1 53 cm Water drains out of a vessel filled with water upto height h through a hole of area A in t seconds If the height of the water is 4 h then how much time will be required for the water to drain out Assume A 4 area of tank 1 t seconds 2 4t seconds 3 21 seconds 4 seconds

In the figure show below there are two tanks I and II with cross sectional area A and A respectively The rate of flow of water between I and II will depend on i h h3 ii h h iii A A 103 h Which of the above options are correct Oil and iii O Only ii O Only i O i and ill A

3 4 m from the tank A square gate of size 4 mx 4 m is hinged at topmost point A fluid of density p fills the space left of it The force which acting 1 m from lowest point can held the gate stationary is 1 2 3 4 128 3 pg 128 pg 9 256 9 pg 256 pg F 1 m

15 On the opposite sides of a wide vertical vess filled with water two identical holes are opened each having cross sectional area a If combined mass of water and vessel is M then find the initial acceleration of tank 1 pagh M 5 alse 2 Smooth 4pagh M

23 If n number of little droplets of water each of radius T and surface tension s coalesce to form bigger drop then pressure inside bigger drop is po is atmosphere pressure 1 3 nT r T Po Po 1 n r 2 4 1 n T r 2T 1 n r Po Po

4 hd g a 3 d hg la 13 A small spherical solid ball is dropped in a viscous liquid The graph correctly represented the velocity v and acceleration a of ball is 3 V a a K K V a 2 4 MA akash Educational Services Limited Regd Office A

anical Properties of Fluids 5 A liquid X of density 3 36 g cm is poured in a U tube which contains Hg Another liquid Y is poured in left arm with height 8 cm upper levels of X and Y are same What is density of Y 8 cm U 0 C 10 cm 200 1

Consider a water tank as shown in the figure It s cross sectional area is 0 4 m The tank has an opening B near the bottom whose cross section area is 1 cm A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom the velocity of water coming out the opening B is v ms The value of v to the nearest integer is Take value of g to be 10 ms 2 24 kg A

A cylindrical container with a hole near bottom plugged with a cork is filled completely with a liquid and placed over a horizontal rough surface Suddenly cork at bottom of cylinder is opened and it is found that the cylinder remains at rest The friction coefficient between cylinder and the surface may be A 100a where A is area of container base and a is area of orifice 0 5 0 8 0 3 All of these

P As the drawing illustrates a pond full of water has the shape of an inverted cone with the tip sliced off and has a depth of 30m The atmospheric pressure above the pond is 1 0 x105Pa The circular top surface radius R and circular bottom surface radius R of the pond are both parallel to th ground The magnitude of the force acting on the top surface by the liquid is the same as the magnitud R2 RI of the force acting on the bottom surface by the liquid Obtain TR Palm 71 R Parm pgk on R R 30 x 10 x 10 30 m 21 R

A U tube is filled with two liquids A and B of densities p and 2p as shown in the figure initially Left arm is closed and air filled above the liquid at atmospheric pressure Po and right arm is open to atmosphere Now liquid of density p is slowly poured in right arm till the level of liquid of density 2p becomes equal in the two arms Neglect any variation in the temperature 11 Height h1 is a ho 12 0 of the system Given 2h Area of cross section of left arm is 2S and that of rig pg arm is S Assume that the length of right arm is sufficiently large Level of liquid B drop in right arm by h h a b 2h 2 b 0 3 3h 2h 3 2h0 0 ho d 4h d 3h 2 MEHHHH 0

luid flows from point P to Q BAD 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 P 1 x 105N m Assume that the air above the water surface expands isothermally the velocity of flow out of the hose when h has decreased to 2m is given by o a m s Fill in OMR sheet Assume ideal fluid flow Pam 105N m 5 h 4m 2 AAAARAHK CHARACHO Hidr HERCHE h 1m1

The amount of liquid flowing per second in the tubes 1 2 and 3 are 10 m s 5 m s and 8 m s respectively The velocity of liquid in the tube 4 having cross section of 0 5 m is 17 m s 3 3 5 m s 2 3 2 14 m s 4 12 m s

ample 5 10 m The volume of the air bubble increases by 10 when it rises from botom to the surface of the water pond If the temperature of the water is constant find the depth of the pond 1 atm of water column

d d 7 32 An open tank 10m long and 2m deep is filled up to 1 5 m height of oil of specific gravity 0 82 The tank is uniformly accelerated along its length from rest to a speed of 20 m s horizontally The shortest time in which the speed may be attained without spilling any oil is g 10 m s A 20 s B 18 s D 5 s C 10 s

7 22 A vessel contains oil density 0 8 gm cm over mercury density 13 6 gm cm A uniform sphere floats with half its volume immersed in mercury and the other half in oil The density of the material of sphere in gm cm is A 3 3 C 7 2 B 6 4 D 12 8

7 25 A large block of ice cuboid of edge length 7 and density Pice 0 9 pw has a large vertical hole along its axis This block Pw is floating in a lake Find out the length of the rope required to raise a bucket of water through the hole A 1 2 C 1 8 B 1 4 D 1 10

7 24 A cubical block of wood of edge 3 cm floats in water The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the container Find the maximum weight that can be put on the block without wetting it Density of wood 800 kg m and spring constant of the spring 50 N m Take g 10 m s XE A 0 1N 1 B 0 35N C 0 5N D 0 7N cellll

A syringe is filled with water Its volume is 20 cm and cross section of its interior part is 4cm The syringe is held vertically such that its nozzle is at its top and its 100g piston is pressed by external agent and moves it with a constant speed The ejected water has a initial upward velocity of 2m s and cross section of the beam of water at the nozzle is 1mm The speed with which the piston is moving is 5 mm sec The external force acting on the piston is 42 N The total work done by external agent in emptying the syringe is 0 095 J The external force remains constant during the process

36 In a cylinder piston arrangement air is under a pressures p A soap bubble of radius r lies inside the cylinder Soap bubble has the surface tension T The radius of soap bubble is to be reduced to half Find the pressure p2 to which air should be compressed isothermally a p 4T c 8p 24T b 4p d p 12T 2T

57 A bent tube of uniform cross section is mounted on a cart which is accelerating towards right with constant acceleration a The total length of the liquid is 2 21 Find the level difference between two limbs in equilibrium a 2 m s 1 10 m a 2 m 45 T b 4 m 45 a c 6 m d 12 m

increasesir excess pressure jo hota hai 2T R vo to surface tension ki wjha se jo pressure hai uske balance kr leta hai to phir net pressure to 5 Excess pressure zeideho cyaed liaccess kyo bolte hai ise The pressure on the concave side of curved liquid surface is greater than that on the convex side Therefore pressure difference exists across two sides of a curved surface This pressure difference is called excess pressure RFACE TENSION TH