Physics1) The vertical limbs of a U shaped tube are filled with a liquid of density upto a height h on each side. The horizontal portion of the U tube having length 2h contains a liquid of density 2. The U tube is moved horizontally with an accelerator g/2 parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs, at steady state will be2) 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 atmosphere pressure at the bottom is

(A) 0.5 kPa (B) 1 kPa(C) 5 kPa (D) None of these

3) A cone of radius R and height H, is hanging inside a liquid of density by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the coin is

4) The area of cross-section of the wider tube shown in figure is 800 cm2. If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :

(A) 10 cm (B) 6 cm (C) 15 cm (D) 2 cm

5) A fluid container is containing a liquid of density is accelerating upward with acceleration a along the inclined place of inclination as shown. Then the angle of inclination of free surface is

6) Figure shows a three arm tube in which a liquid is filled upto levels of height l. It is now rotated at an angular frequency about an axis passing through arm B. The angular frequency at which level of liquid in arm B becomes zero

7) An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was

(A) g/3 (B) 2g/3 (C) 3g/2 (D) None

8) A liquid of mass 1 kg is filled in a flask as shown in figure. The force exerted by the flask on the liquid is (g = 10 m/s2)[Neglect atmospheric pressure]:

(A) 10 N (B) greater than 10N(C) less than 10N (D) zero

9) In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2and 3. The height h for the equilibrium of cylinder must be

10) The pressure at the bottom of a tank of water is 3P where P is the atmospheric pressure . If the water is drawn out till the level of water is lowered by one fifth., the pressure at the bottom of the tank will now be

(A) 2P (B) (13/5) P (C) (8/5) P (D) (4/5)P11) An open-ended U-tube of uniform cross-sectional area contains water (density 1.0 gram/centimeter3) standing initially 20 centimeters from the bottom in each arm. An immiscible liquid of density 4.0 grams/ centimeter3 is added to one arm until a layer 5 centimeters high forms, as shown in the figure above. What is the ratio h2/h1 of the heights of the liquid in the two arms?

(A) 3/1 (B) 5/2 (C) 2/1 (D) 3/212) Two cubes of size 1.0 m sides, one of relative density 0.60 and another of relative density = 1.15 are connected by weightless wire and placed in a large tank of water. Under equilibrium the lighter cube will project above the water surface to a height of

(A) 50 cm (B) 25 cm (C) 10 cm (D) zero13) A cubical piece of wood has dimensions a, b and c. Its relative density is d. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of SHM executed by it is

14) A slender homogeneous rod of length 2L floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75. The length of rod that extends out of water is

15) A container of large surface area is filled with liquid of density r. A cubical block of side edge a and mass M is floating in it with four-fifth of its volume submerged. If a coin of mass m is placed gently on the top surface of the block is just submerged. M is

(A) 4m/5 (B) m/5 (C) 4m (D) 5m

16) Two cyllinders of same cross-section and length L but made of two material of densities d1 and d2 are cemented together to form a cylinder of length 2L. The combination floats in a liquid of density d with a length L/2 above the surface of the liquid. If d1 > d2 then:

17) A piece of steel has a weight W in air, W1 when completely immersed in water and W2 when completely immersed in an unknown liquid. The relative density (specific gravity)of liquid is:

18) A small wooden ball of density r is immersed in water of density s to depth h and then released. The height H above the surface of water up to which the ball will jump out of water is

19) A cylindrical tank of height 1 m and cross section area A = 4000 cm2 is initially empty when it is kept under a tap of cross sectional area 1 cm2. Water starts flowing from the tap at t = 0, with a speed = 2 m/s. There is a small hole in the base of the tank of cross-sectional area 0.5 cm2. The variation of height of water in tank (in meters) with time t is best depicted by

20) A non viscous liquid of constant density 500 kg/m flows in a variable cross-sectional tube. The area of cross-section of the tube at two points P and Q at heights of 3 m and 6 m are 2 x 10-3 m3 and 4 x 10-3 m3 respectively. The work done per unit volume by the forces of gravity as the fluid flows from point P to Q, is(a) 29.4 J/m3 (b) - 1.47 x 104 J/m3 (c) - 2.94 x 104 J/m3 (d) none of these

21) A block weighs 15 N and 12 N in air and water respectively. When it is immersed in another liquid, it weighs 13 N, then the relative density of the block is

(a) 5 (b) 6 (c) 10 (d) 2(5) 4

22) As the figure shows, S1 and S2 are spring balances. A block A is hanging from spring balance S) and immersed in a liquid L which is contained in a beaker B. The mass of a beaker B is 1 kg and mass of liquid L is 1.5 kg. The S1 and S2 balances read 2.5 kg and 7.5 kg respectively. What will be the readings of S1 and S2 when block A is pulled up out of the liquid?

(a) S1 will read 5 kg and S2 will read 5 kg (b) S1 will read 7.5 kg and S2 will read 2.5 kg (c) S1 will read 2.5 kg and S2 will read 7.5 kg (d) S1 will read 10 kg and S2 will read 2.5 kg

23) A body having volume V and density is attached to the bottom of a container as shown. Density of the liquid is d(>). Container has a constant upward acceleration a. Tension in the string is

24) In a cylindrical vessel containing liquid of density , there are two holes in the side walls at heights of h1 and h2 respectively such that the range of efflux at the bottom of the vessel is same. The height of a hole, for which the range of efflux would be maximum, will be

25) Equal volumes of two immiscible liquids of densities and 2are filled in a vessel as shown in figure. Two small holes are punched at depth h/ 2 and 3h/2 from the surface of lighter liquid. If v1 and v2 are the velocities of a flux at these two holes, then v1/v2 is :

(26) The three water filled tanks shown have the same volume and height. If small identical holes are punched near this bottom, which one will be the first to get empty.

(A) (i) (B) (ii)(C) (iii) (D) All will take same time

(27) A U-tube of uniform cross-sectional area and open to the atmosphere is partially filled with mercury. Water is then poured into both arms. If the equilibrium configuration of the tube is as shown in Figure P15.19, with h2 = 1.00 cm, determine the value of h1 .

28) A Styrofoam slab has a thickness of 10.0 cm and a density of 300 kg/m3. When a 75.0-kg swimmer is resting on it, the slab floats in fresh water with its top at the same level as the waters surface. Find the area of the slab.

29) A Styrofoam slab has thickness h and density S . What is the area of the slab if it floats with its upper surface just awash in fresh water, when a swimmer of mass m is on top

30) Mercury is poured into a U-tube, as shown in FigureP15.18a. The left arm of the tube has a cross-sectional area A1 of 10.0 cm2, and the right arm has a cross-sectional area A2 of 5.00 cm2. One-hundred grams of water are then poured into the right arm, as shown in Figure P15.18b. (a) determines the length of the water column and find h.

31) A frog in a hemispherical pod finds that he just floats without sinking into a sea of blue-green ooze having a density of 1.35 g/cm3 (Fig. P15.28). If the pod has a radius of 6.00 cm and a negligible mass, what is the mass of the frog?

32) A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.20 * 104 kg. To dive, this submarine takes on mass in the form of seawater. Determine the amount of mass that the submarine must take on if it is to descend at a constant speed of 1.20 m/s, when the resistive force on it is 1 100 N in the upward direction. Take 1.0*103 kg/m3 as the density of seawater

33) A water hose 2.00 cm in diameter is used to fill a 20.0-L bucket. If it takes 1.00 min to fill the bucket, what is the speed v at which water moves through the hose? (Note: 1 L =1 000 cm3.) (b) If the hose has a nozzle 1.00 cm in diameter, find the speed of the water at the nozzle.

34) A horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 *104 Pa and the pressure in the smaller pipe is 6.00 *104 Pa, at what rate does water flow through the pipes?

35) A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 * 10-3 m3/min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

36) A siphon is used to drain water from a tank, as illustrated in Figure P15.43. The siphon has a uniform diameter. Assume steady flow without friction. (a) If the distance h 1.0 m, find the speed of outflow at the end of the siphon. (b) What is the limitation on the height of the top of the siphon above the water surface?(For the flow of liquid to be continuous, the pressure must not drop below the vapor pressure of the liquid.)

37) A hypodermic syringe contains a medicine with the density of water (Fig. P15.44). The barrel of the syringe has a cross-sectional area A =2.50 * 10-5 m2, and the needle has a cross-sectional area a =1.00 * 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F of magnitude 2.00 N acts on the plunger, making the medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needles tip.

38) A helium-filled balloon is tied to a 2.00-m-long, 0.050 0-kg uniform string. The balloon is spherical with a radius of 0.400 m. When released, the balloon lifts a length h of string and then remains in equilibrium, as shown in Figure P15.49. Determine the value of h. The envelope of the balloon has a mass of 0.250 kg.

39) Water is forced out of a fire extinguisher by air pressure, as shown in Figure P15.50. How much gauge air pressure in the tank (above atmospheric) is required for the water jet to have a speed of 30.0 m/s when the water level is 0.500 m below the nozzle?

40) Figure P15.48 shows a tank of water with a valve at the bottom. If this valve is opened, what is the maximum height attained by the water stream exiting the right side of the tank? Assume that h=10 m L = 2 m , and = 300 , and that the cross-sectional area at point A is very large compared with that at point B.

(41)Write down the Bernoullis equation for a fluid flow(a) State the conditions under which the Bernoullis equation valid(b) Show that the above equation dimensionally correct

A U-tube open at both ends is partially filled with water (Fig. P15.69a). Oil having a density of 750 kg/m3 is then poured into the right arm and forms a column L =5.00 cm in height (Fig. P15.69b).

(a) Determine the difference h in the heights of the two liquid surfaces. (b) The right arm is shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. P15.69c). Determine the speed of the air being blown across the left arm. (Take the density of air as 1.29 kg/m3.)

42) The drinking water needs of an office are met by large water bottles. One end of a 0.25cm diameter plastic hose is inserted into the bottle placed on a high stand, while the other end an on/of valve is maintained 60cm below the bottom of the bottle. If the water level in the bottle is 45cm when it is full.1) Determine how long will it take at the minimum to fill an glass of volume 200cm-32) When the bottle almost empty

43) Calculate static and dynamic pressures

44) Write down the Bernoullis equation for a fluid flowState the conditions under which the Bernoullis equation validShow that the above equation dimensionally correct

45) Write down the Bernoullis equation for a fluid flowState the conditions under which the Bernoullis equation validShow that the above equation dimensionally correctAir is drawn into a wind tunnel used for testing automobile as shown below Fig P3.27 and density of the oil is 900 kgm-3 and height of the oil column is 2cm.1) Determine the nanometer reading h when the velocity in the test section is 60kmh-1. 2) Determine the difference between the stagnation pressure on the front of the automobile and the pressure in the test section

46) Water flows from a large tank through a large pipe that splits into two smaller pipes of diameter 0.02m and 0.03 respectively as shown below picture Fig P3.83. if viscous effect are negligible, determine the flowrate from the tank and the pressure at point (1)

a) Determine the maximum height attain by the water

47) Write down the Bernoullis equation for a fluid flowState the conditions under which the Bernoullis equation validShow that the above equation dimensionally correctDuring trip to the beach( Patm atm) a car runs out of gasoline and it become necessary to siphon gas out of the car of a good Samaritan. The siphon is small diameter hose, and to start the siphon it is necessary to insert one siphon end into the full gas tank, fill the hose with gasoline via suction, and then place the other end in a gas can below the level of the gas tank. The pressure different between point 1 and point 2 will cause the liquid to flow from the higher to the lower elevationa) The minimum time to withdraw 4Lof gasoline from the tank to can end b) The pressure at point 3 the density of gasoline is 750kgm-3

Harshana Perera(B.Sc(Phy),BIT,SCJP)2014 T KitTurn Over