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Fluid statics overview, , Laws of pressure, , 1. A liquid can exactly change its shape but a solid, can not because, (a) the density of a liquid is smaller than that of a, solid, (b) the forces between the molecules is stronger, in solid than in liquids

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(c) the atoms combine to form bigger molecules, in a solid, (d) the average separation between the, molecules is larger in solids., 2., , In a case of a liquid, (a) only bulk modulus is defined, (b) only bulk modulus and Young’s modulus are, defined, (c) only bulk modulus and shear modulus are, defined, (d) all the three modulii (bulk, Young’s and, shear)are defined, , 3. Two, liquids, which do not, react chemically, 2, h2, are placed in a, h1, bent tube as, shown in the 1, figure., The, heights of the liquids above their surface of, separation are, (a) directly proportional to their densities, (b) inversely proportional to their densities, (c) directly proportional to square of their, densities, (d) equal, 4. Equal mass of three liquids are kept in three, identical cylindrical vessels A, B and C. The, densities are A, B, C with A < B < C. The, force on the base will be, (a) maximum in vessel A, (b) maximum in vessel B, (c) maximum in vessel C, (d) equal in all the vessels, 5. A wooden object floats, in water kept in a, beaker. The object is, near a side of the, beaker (figure). Let P1, A, C, B, P2, P3 be the pressures at the three points A, B, and C of the bottom as shown in the figure., (a) P1= P2 = P3, (b) P1 < P2 < P3, (c) P1 > P2 > P3, (d) P2 = P3  P1, 6. A piece of wood is floating in water kept in a, bottle. The bottle is connected to an air pump., Neglect the compressibility of water. When, more air is pushed into the bottle from the pump,, the piece of wood will float with, (a) larger part in the water(b) lesser part in the, water (c) same part in the water (d) it will sink, , 7. A beaker containing a liquid is kept inside a big, closed jar. If the air inside the jar is continuously, pumped out, the pressure in the liquid near the, bottom of the liquid will, (a) increase, (b) decrease, (c), remain constant, (d) first decrease and then increase, 8. The hydrostatic difference in blood pressure in a, person of height 1.83 m between his brain and, foot, assuming that the density of blood is, 1.06x103 kg/m3 is, (a) 1.90 x 103 Pa, (b) 1.90 x 104 Pa, (c) 19.0 x 104 Pa, (d) 1.90 x 104 Pa, 9. Suppose the pressures at the surface of mercury, in a barometer tube is P1 and the pressure at the, surface of mecrury in the cup is P2., (a) P1 = 0, P2 = atmospheric pressure, (b) P1 = atmospheric pressure, P2 = 0, (c) P1 = P2 = atmospheric pressure, (d) P1 = P2 = 0, 10. A barometer tube reads 76 cm of mercury. If the, tube is gradually inclined at an angle of 60° with, vertical, keeping the open end immersed in the, mercury reservoir, the length of the mercury, column will be, (a) 152 cm (b) 76 cm (c) 38 cm(d) 38 3 cm, , 11. A U-tube of uniform cross section (see Fig) is, partially filled with a liquid I. Another liquid II, which does not mix with liquid I is poured into, one side. It is found that the liquid, І, ІІ, levels of the two sides of the tube, are the same, while the level of, liquid I has risen by 2 cm. If the, specific gravity of liquid is 1.1, the, specific gravity of liquid II must be, (a) 1.12, (b) 1.1, (c) 1.05, (d) 1.0, 12. Equal masses of water and a liquid of density 2, are mixed together, then the mixture has a, density of, (a) 2/3, (b) 4/3, (c) 3/2, (d) 3, 13. Pressure at a point inside a liquid does not, depend on:, a. The depth of the point below the surface of, the liquid, b. The nature of the liquid, c. The acceleration due to gravity at that point, d. The shape of the containing vessel

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14. Two stretched membranes of area 2cm2 and 3, cm2 are placed in a liquid at the same depth. The, ratio of the pressure on them is:, (a) 1:1, (b) 2:3, (c) 3:2, (d) 22 : 32, 15. A dam for water reservoir is built thicker at the, bottom than at the top because:, a. Pressure of water is very large at the bottom, due to its large depth, b. Water is likely to have more density at the, bottom due to its large depth, c. Quantity of water at the bottom is large, d. None of these, e., 16. A vessel contains liquid of density  as shown in, figure. The gauge pressure at the point P is:, , (a) h  g, (c) ( H  h)  g, , (b) h g, (d) ( H  h)  g cos, , 17. A tank 5m high is half filled with water and then, is filled to the top with oil of density 0.85 g/cm3., The pressure at the bottom of the tank, due to, these liquids, is:, (a) 1.85X103 g/cm2 (b) 89.25 X103 g/cm2, (c) 462.5 X103 g/cm2, (d) 500 X103 g/cm2, 18. A U-tube is partially filled with water. Oil,, which does not mix with water, is next poured, into one side until water rises by 25 cm on the, other side. If the density of oil be 0.8, the oil, level will stand higher than the water level by:, (a) 6.25 cm, (b) 12.50 cm, (c) 31.25 cm, (d) 20 cm, 19. The height to which a cylindrical vessel be filled, with a homogeneous liquid to make the average, force with which the liquid presses the side of, the vessel equal to the force exerted by the liquid, on the bottom of the vessel, is equal to:(neglect, atmospheric pressure), a. Half of the radius of the vessel, b. Radius of the vessel, c. One – Fourth of the radius of the vessel, d. Three – fourths of the radius of the vessel, 20. Pressure is applied to an enclosed fluid. It is:, a. Increased and applied to every part of the, fluid, b. Diminished and transmitted to the walls of, the container, , c. Increased in proportion to the mass of the, fluid and then transmitted, d. Transmitted unchanged to every portion fo, the fluid and the walls of container, 21. Pressure applied to an enclosed fluid is, transmitted undiminished to every portion of the, fluid and the walls of the containing vessel. This, law was first formulated by:, (a) Bernoulli, (b) Archimedes, (c) Boyle, (d) Pascal, 22. A piston of cross – sectional area 100 cm2 is, used in a hydraulic press to exert a force of 107, dyne one water. The cross – sectional area of the, other piston which supports an object having a, mass 2000 kg is:, (a) 100 cm2, (b) 109 cm2, 4, 2, (c) 2 x 10 cm, (d) 2 x 1010 cm2, 23. As a bubble comes from the bottom of a lake to, the top, its radius:, (a) Increases, (b) Decreases, (c) Does not change, (d) Becomes zero, 24. When a large bubble rises from the bottom of a, lake to the surface, its radius doubles. The, atmospheric pressure is equal to that of a column, of water of height H. The depth of the lake is:, (a) H, (b) 2H, (c) 7H, (d) 8H, 25. The pressure of water at bottom in a lake is, 3 times that at half depth where the water, 2, , barometer reads 10m. The depth of the lake is:, (a)5m, (b) Infinite, (c) 20m, (d) 10m, 26. Two communicating vessels contain mercury., The diameter of one vessel is four times larger, than the diameter of the other. A column of, water of height h0 = 70 cm is poured into the left, – hand vessel (the narrower one). How much, will be mercury level rise in the right – hand, vessel? (Specific density of mercury = 13.6)., (a) 0.3 cm (b) 0.7 cm (c) 0.1 cm (d) 1.0 cm, , 27. A hydrogen balloon released on the moon, would:, a. Climb up with an acc. Of 9.8 m/sec2, b. Climb up with an acc. Of 9.8 m x 6 m/sec2, c. Neither climb nor fall, d. Fall with an acc. Of (9.8/6) m/sec2, 28. An iron ball is weighed in air and then in water, by a spring balance:, a. Its weight in air is more than in water

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b. Its weight in water is more than in air, c. Its weight is same both in air and water, d. Its weight is zero in water, 29. A glass bulb is balanced by a brass weight in a, sensitive beam balance. Now the balance is, covered by a bell-jar which is then evacuated;, then:, a. The beam will remain horizontal, b. The pan containing the bulb will go down, c. The pan containing the bulb will go up, , [Archimedes’s Principle], , 33. A balloon of mass 8 kg and volume V is filled, with helium (rHe = 0.178 kg/m3). If it has to lift, a 42 kg load, V should be (density of air = 1.29, kg/m3), (a) 45 m3, (b) 4.5 m3, 3, (c)90m, (d)135 m3, 34. A balloon has volume of 1000 m3. It is filled, with hydrogen (r = 0.09 g/litre). If the density of, air is 1.29 g/litre. It can lift a total weight of, (a) 600 kg, (b) 1200 kg, (c) 300 kg, (d) 1800 kg, 35. A 20 N metal block is suspended by a spring, balance. A beaker containing some water is, placed on a weighing machine which reads 40 N., The spring balance is now lowered so that the, block gets immersed in the water. The spring, balance now reads 16 N. The reading of the, weighing machine will be, (a) 36 N, (b) 60 N (c) 44 N, (d) 56 N, 36. A piece of alloy consisting of gold and silver, weight 20 g in air and 18.5 g in water. If the, specific gravities of gold and silver are 19.3 and, 10.5 respectively, the quantity of gold in the, alloy is, (a) 9.3 g (b) 13.9 g (c) 4.65 g (d) 5.53 g, , 30. Specific gravity of ice is 0.918. A piece of ice, floats in salted water (sp. gr. = 1.03) such that, 0.224 litre of its volume is above the surface of, water. The total volume of the piece of ice is, (a) 3.09 litre, (b) 4.12 litre, (c) 1.03 litre, (d) 2.06 litre, 31. A rubber balloon has 200 gm of water in it. Its, weight in water will be (neglect the weight of, balloon), (a) 100 gm (b) 200 gm(c) 50 gm (d) zero, 32. A ball floats on the surface of water in a, container exposed to the atmosphere. Find the, correct statement among the following, (b) The ball remains immersed a little more, than its former depth when the container, is covered and the air is removed, (c) The balls sinks when the container is, covered and the air is removed, (d) The ball rises a little when the container, is covered and the air is compressed, (e) The ball remains at its former depth, regardless of whether it is covered and, the air is removed or whether the air is, compressed., (f), , 37. Raft of wood, density 600kg/m3,of mass 120kg, floats in water. How much weight can be put on, the raft to make it just sink?, [a]200kg [b]40kg [c]120kg, [d]80kg, 38. boy is carrying a bucket of water in one hand, and a piece of plastic in the other hand . after, transferring the plastic piece to the bucket the, boy will carry, [a]more load than before, [b]less load than before, [c]same load as before, [d]either less or more load depending on the, density of the plastic, 39. Then pressure is applied through a hole in the, top of a closed tube containing water, the, pressure is transmitted to :, [a]only the bottom of container, [b]all directions, [c]only the side faces and the bottom of the, container, [d]only the side of the container., 40. A block of ice is floating on water contained in a, beaker .when all the ice melts, the level of water, [a]rises, [b]falls, [c]remains unchanged, [d]none

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41. 1 kg of cotton and iron in air are transferred to, vacuum and weighted again then, [a]cotton and iron will weigh same, [b]iron will weigh more than cotton, [c]cotton will weigh more than iron, [d] none of the above, 42. An ice-berg is floating in sea water.what, percentage of volume of the ice-berg is above, the water?[relative destiny of sea water =1.20, and relative density of ice =0.9], [a]20% [b]25% [c]33.3%, [d]50%, 43. Two bodies of equal volume A and B float on, water in equilibrium 2/3 of the volume of A and, half the volume of B is inside water. The ratio of, densities of A and B is, [a]1:3, [b]3:2, [c]3:4, [d]4:3, 44. A small block of wood of relative destiny 0.5 is, submerged in water at a depth of 5 m. when the, block is released ,it starts moving upwards, the, acceleration of the block is[g=10ms-2], [a]5ms-2 [b]10ms-2 [c]7.5ms-2 [d]15ms-2, 45. Water stands upto a height h behind the vertical, wall of a dam. What is the horizontal force, pushing the dam downstream if the width of the, dam be b:, [a]hbpg, [b]hbpg/2, [c]hbpg/4, [d]hbpg/6, 46. A body floats in a liquid, contained in a beaker. The, whole system as shown in a, figure falls freely under, gravity. The upthrust on the, body is, (g) zero, (h) equal to the weight of the liquid, displaced, (i) equal to the weight of the body in air, (j) equal to the weight of the immersed, potion of the body, A, (k), 47. The spring balance A, m, B, reads 2 kg with a block m, suspended from it. A, balance B reads 5 kg when a beaker with liquid, is put on the pan of the balance. The two, balances are now so arranged that the hanging, mass is inside the liquid in the beaker as shown, in the figure. In this situation:, (l) the balance A will read more than 2 kg, , (m) the balance B will read less than 5 kg, (n) the balance A will read less than 2 kg and, B, (o) will read more than 5 kg, (p) the balance A and B will read 2 kg and 5, kg respectively, 48. A jar is filled with two non-mixing liquids 1 and, having densities ρ1 and, ρ2, respectively. A solid ball,, Liquid 1 ρ1, made of a material of, ρ3, density ρ3, is dropped in the, Liquid 2 ρ2, jar. It comes to equilibrium, in the position shown in the, figure. Which of the following is true for ρ1, ρ2, and ρ3?, (a) ρ3< ρ1 < ρ2, (b) ρ1> ρ3 > ρ2, (c) ρ1< ρ2 < ρ3, (d) ρ1< ρ3 < ρ2, 49. When a body is wholly or partially immersed in, a liquid it appears to lose weight. This loss of, weight is equal to the weight of:, (q) Water displaced by the body, (r) Liquid displaced by the body, (s) Equal volume of water, (t) Equal volume of liquid, 50. Two pieces of metal when immersed in a liquid, have equal upthrust on them; then:, (u) Both pieces must have equal weights, (v) Both pieces must have equal densities, (w) Both pieces must have equal volumes, (x) Both are floating to the same depth, 51. If there were a smaller gravitational effect,, which of the following forces do you think, would alter in some respect:, (a) Viscous force, (b) Archimedes, suplift, (c) Electrostatic force (d) Nuclear force, 52. A body floats in a liquid contained in a beaker., The whole system as shown in, fig. Falls freely under gravity., The upthrust on the body due, to the liquid is:, (y) zero, (z) Equal to the weight of the liquid, displaced, (aa) Equal to the weight of the body in air, (bb) Equal to the weight of the immersed, portion of the body, 53. When a body is weighed in a liquid, the loss in, its weight depends upon:, (a) Volume of the body

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(b) Mass of the body, (c) Shape of the body, (d) CG of the body, , (a) Remain in the same position, Rise up, (c) Move down, , 54. Which of the following would a hydrogen, balloon find easier to lift:, (a) 1 kg of water, (b) 1 kg of steel, (c) 1 kg of light packed feather, (d) All the above, 55. A body weighs 40g in air. If its volume is 10cc., In water it will weigh:, (a) 30g, (b) 40g, (c) 50g, (d) Data are insufficient to calculate, 56. A block of metal (density 7 g/cc) of size 5cm x 5, cm x 5 cm is weighed completely submerged in, water. What will be its apparent weight (density, of water = 1 g/cc):, (a) (6 x 5 x 5 x 5)g (b) (4  4  4  7)g, (c) (7  5  5  5)g, (d) (4  4  4  6)g, 57. A weightless rubber balloon has 100g of water, in it. Its weight in water will be:, (a) 100g (b) 200g (c) 50g (d) zero, , (b), , 61. A vessel with water is placed on a weighing pan, and reads 600g. Now a ball of 40g and density, 0.80 g/cc is sunk into the water with a pin as, shown in fig. Keeping it sunk. The weighing pan, will show a reading:, (a) 600g (b) 550g (c) 650g (d) 632g, 62. A beaker of water kept in the left pan of a, common balance is counter poised with weights, in the right pan. Now a body of mass 12 g and, density 3g/cc is suspended inside the beaker, from an independent support and the body is, completely immersed weight to be added in the, right pan will be:, (a) Zero (b) 8g, (c) 12g, (d) 4g, 63. A boy carries a fish in one hand and a bucket of, water in the other hand; if he places the fish in, the bucket, the weight now carried by him:, (a) is less than before (b) is more than, before, (c) is the same as before, (d) depends upon his speed, , 58. A fisherman hooks an old log of wood of weight, 12N and volume 1000 cm3. He pulls the log half, way out of water. The tension in the string at this, instant is:, (a) 12N, (b) 8N, (c) 10N, (d) 7N, , 64. A boy of weight W1 displaced an amount of, water W2. When floating:, (a) W1  W2, (b) W1  W2, (c) W2  W1, (d) any of (a), (b) and (c), , 59. The reading of a spring balance when a block is, suspended from it in air is 60N. This reading is, changed to 40N when the block is submerged in, water. The specific gravity of the block must, therefore be:, (a) 3, (b) 2, (c) 6, (d) 3/2, , 65. It is easier to swim in sea water than in river, water because:, (cc) Sea is wider than the river., (dd) Sea is deeper than the river, (ee) Density of sea water is greater than, that of river, (ff) Sea is having high waves all the time, , 60. A beaker containing water is counter poised on a, balance. If a finger is immersed in water so that, it does not touch the bottom or the side of the, beaker, the pan on which the beaker rests will:, , Fluid-2 Fluid dynamics, , Fluid dynamics (overview)

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Single choice questions, 1. Water enters through end A with a speed v1 and, leave through end B with a speed v2 of a, cylindrical tube AB. The tube is always, completely filled with water., In case I the, tube is horizontal, in case II it is vertical with, the end A upward and in case III it is vertical, with the end B upward. We have v1 = v2 for, (a) case I (b) case II (c) case III, (d), each case, 2. Bernoulli’s theorem is based on conservation of, (a) momentum, (b) mass, (c) energy, (d) angular momentum, 3. Water is flowing through a long horizontal tube., Let PA and PB be the pressures at two points A, and B of the tube, (a) PA must be equal to PB, (b) PA must be greater than PB, (c) PA must be smaller than PB, (d) PA = PB only if the crosssectional area at A, and B are equal, , 5., , 6. Water and mercury are filled in two cylindrical, vessels upto same height. Both vessels have a, hole, in the wall near the bottom. The velocity of, water, and mercury coming out of the holes are v1 and, v2, respectively, (a) v1 = v2, (b) v1 = 13.6 v2, (c) v1 = v2/13.6, (d) v2 = 13.6 v2, 7., , 4. Water is following through a tube of non, uniform, cross section. at the extreme narrow portion of, the, pipe, the water will have, (a) maximum speed and least pressure, (b) maximum pressure and least speed, (c) both pressure and speed maximum, (d) both pressure and speed least, , In a streamline flow, (a) the speed of a particles at a particular point, is same as the previous particle passed from, that point, (b) the velocity of a particle always remains, same, (c) the kinetic energies of all the particles, arriving at a given point are the same, (d) the moments of all the particles arriving at, a given point are the same, , A large cylindrical tank has a hole of area A at, its bottom. Water is poured in the tank by a, tube of, equal crosssectional area A ejecting water at, the speed v., (a) the water level in the tank will keep on, rising, (b) no water can be stored in the tank, (c) the water level will rise to a height v²/2g, and then stop, (d) the water level will oscillate

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8., , A tank containing water has an orifice on one, vertical side. If the centre of orifice is 4.9 m, below, the surface level on the tank, the velocity of the, discharge of water is (assume no wastage of, energy), (a) 19.6 m/s(b) 14.7 m/s(c) 9.8 m/s (d) 4.9 m/s, , 9. Water flows along a horizontal pipe of which the, cross-section is not constant. The pressure is 1, cm of Hg where the velocity is 35cm/s. At a, point where the velocity is 65 cm/s, the, pressure will be, (a) 0.89 cm of Hg, (b) 8.9 cm of Hg, (c) 0.5 cm of Hg, (d) 1 cm of Hg, 10. A cylindrical drum, open at the top, contains 30, litres of water. It drains out through a small, opening at the bottom. 10 litres of water, comes out in time t1, the next 10 litres in, further time t2 and the last 10 litres, in further time t3. Then,, (a) t1 = t2 = t3, (b) t1 > t2 > t3, (c) t1 < t2 < t3, (d) t2 > t1 = t3., 11. The pressure that will be built by a compressor, in a paint gun if a stream of liquid paint flows, out of it with a velocity of 25 m/s (density of, paint is 0.8 g/cc) is, (a) 2.5 x 103 N/m² (b) 2.5 x 102 N/m², (c) 5x105 N/m², (d) 2.5 x 105 N/m², 12. Two water pipes of diameters 2cm and 4cm are, connected with the main supply line .the, velocity of, flow of water in the pipe of 2cm diameter is, (a) 4times that in the other pipe, (b) 1/4 times that in the other pipe, (c) 2times that in the other pipe, (d) 1/2times that in the other pipe, 13. An incompressible liquid flows through a, horizontal, v2=1.5m/s, A, tube at shown, A, in the, v1=3m/s, following fig., then the, 1.5A, v, velocity v of, the fluid is, (a)3.0m/s (b)1.5m/s (c)1.0m/s (d)2.25m/s, 14. In this figure, an ideal liquid, flows through the tube,, which is of uniform cross, , A, B, , section. the liquid has velocities, Ua and Ub and pressure Pa and, Pb A and B respectively, (a)Ua=Ub (b)Ub>Ua (c)Pa=Pb (d)Pb>Pa, 15. A cylindrical, vessel of, 90 cm, height is, kept filled, upto the, brim it has, four holes 1,2,3,4 which are respectively at, heights of 20cm, 30cm ,45cm and, 50cm from the horizontal floor PQ. the water, falling at the maximum horizontal distance, from the vessel comes from, (a) hole number 4, (b) hole number 3, (c) hole number 2, (d) holenumber1diagram, 16. A rectangular vessel when full of water takes 10, minutes to be emptied through an office in its, bottom, how much time will it take to be, emptied when half, filled with water, (a)19 minute, (b)7 minute, (c)5minute, (d)3minute, 17. The area of cross-section at two points in a pipe, are A1 and A2 where a venturimeter (to show, pressure difference) is connected, indicating, p as the, difference in pressure at two, points. If the density of fluid flowing through, the pipe is , the quantity of fluid flowing in, one second is, (a), (c), , 2p, (A12  A 22 ), A1A 2, , , (b) A1A2, , 2A1A 2, 2p, (d), 2, 2, , (A1  A 2 ), , 2p, (A12  A 22 ), 2p, (A12  A 22 ), , 18. Water is filled in a container upto height 3m., A small hole of area ‘a’ is punched in the, wall of the container at a height 52.5 cm from the, bottom. the cross sectional area of the container is, A. If a/A = 0,1 then v2 is (where v is the velocity of, water coming out of the hole), (a) 50, (b) 51, (c) 48, (d) 51.5, 19. Water from a tap emerges vertically downwards, with an initial speed of 1.0 m/s. The crosssectional area of tap is 10–4 m2. Assume that, the pressure is constant throughout the stream, of water and that the, flow is steady, the, cross-sectional area of stream 0.15 m below, the tap is:, (a) 5.0 × 10–4 m2, (b) 1.0 × 10–5 m2

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(c) 5.0 × 10–5 m2, , (d) 2.0 × 10–5 m2, 25., , A glass plate of area 20 cm² is separated from, another larger plate of glass by a 1 mm thick, layer of viscous fluid whose viscosity is 20, poise. If the smaller plate is to be moved over, the larger one with a velocity of 2 cm/s, the, force required to keep it moving is, (a) 4 x 104 N (b) 4 x 103 N (c) 0.4 N (d), 0.08 N, , 26., , A drop of water of radius 0.01 cm is falling, through the atmosphere ( = 1.20 kg/m3 and , = 1.8 x 105 N.s/m²). If the density of water is, 1 x 103 kg/m3, the terminal velocity of the, water drop is, (a) 1.2 m/s, (b) 2.1 m/s, (c) 1.2 x 102 m/s, (d) 2.1 x 102 m/s, A steel ball of radius 1 mm falls in a tank of, glycerine. If the densities of steel and glycerine, are .5 and 1.32 g/cc respectively and the, viscosity of glycerine is 8.3 poise, the terminal, velocity of the ball is, (a) 18 cm/s(b) 8.1 cm/s(c)1.8 cm/s (d) 3.6 cm/s, , Viscosity, 20., , A sphere is falling in a viscous fluid. Its, velocity will, (a) increase as it goes down and will come to a, stop after attaining the maximum velocity, (b) decrease as it goes down as viscous forces, cause retardation, (c) attain a velocity after which it becomes, constant, (d) remains constant throughout., , 21. In which one of the following cases will the, liquid flow in a pipe be most stream lined, (a) liquid of high viscosity and high density, flowing through a pipe of small radius, (b) liquid of high viscosity and low density, flowing through a pipe of radius, (c) liquid of low viscosity and low density, flowing through a pipe of large radius, (d) liquid of low viscosity and high destiny, flowing through a pipe of large radius, 22., , When a sphere falling in a viscous fluid attains, the terminal velocity, then, (a) the net force on the sphere acts downwards, (b) the viscous retarding force plus the buoyant, force, equals the weight of the sphere, (c) the viscous retarding force plus the weight of, the sphere equals the buoyant force, (d) the buoyant force is zero and the viscous, force equals the weight of the sphere., , 23., , Two spheres of the same material but of radii, 0.01 m and 0.02 m are dropped only by one in, the same viscous find. Their terminal, velocities respectively will be, (a) the same for the two spheres, (b) in the ratio of 1 to 2, (c) in the ratio of 1 to 4, (d) in the ratio of 4 to 1, , 24., , If the Reynolds number NR for water at 20°C, in CGS units is 1000, its value in SI unit shall, be, (a) 1000 x 105 (b) 105 (c) 1000 (d) 1000 x 103, , 27., , 28., , Water flows in a tube of diameter 2 cm ( = 1, x 103 N.s/m²) so that the flow is streamline. If, the Reynolds number of streamline flow is, 2000, the maximum average velocity of water, is, (a) 0.1 m/s(b) 1 m/s (c) 0.5 m/s (d) 0.2 m/s, , 29. A good lubricant should have, (a) high viscosity, (b) low viscosity, (c) moderate viscosity, (d) high density, 30. Spherical balls of radius ‘R’ are falling in a, viscous fluid of viscosity ‘’ with a velocity, ‘v’. The retarding viscous force acting on the, spherical ball is, (a) inversely proportional to both radius ‘R’ and, velocity ‘v’., (b) directly proportional to both radius ‘R’ and, velocity ‘v’., (c) directly proportional to ‘R’ but inversely, proportional to ‘v’., (d) inversely proportional to ‘R’ but directly, proportional to velocity ‘v’.

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SURFACE TENSION, Surface Tension (Overview), , Single choice questions, 1. A square loop of wire 6 cm on a side is suspended, from a thread by fastening the thread at the, middle of one side. The loop is then lowered, into water. It is subsequently raised slowly so, as to form a film of water. If the surface, tension of water is 75x103 N/m, the upward, force required to break the film is, (a) 1.8 x 102 N, (b) 9 x 103 N, (c) 9 x 104 N, (d) 6 x 103 N, 2. Surface tension is due to, (a) Frictional forces between molecules, (b) Cohesive forces between molecules, (c) Adhesive forces between molecules, (d) Gravitational forces, , (a) only on the cohesive force of the liquid, molecules (b) only on the adhesive force, between the, molecules of the glass and liquid, (c) only on relative cohesive and adhesive force, (d) neither on cohesive nor on adhesive force, 6. Force necessary to pull a circular plate of 5cm, radius from water surface for which surface for, which surface tension is 75 dynes /cm is, (a)30dyne (b)60dyne (c)750dyne (d)750dyne, 7. The property of surface tension is obtained in, (a) solids, liquid and gasses, (b) liquids, (c) gasses, (d) matter, , 3. A pin or a needle floats on the surfaces of water,, the reason for this, (a)surface tension, (b)less weight, (c)up thrust of liquid, (d)none of the, above, , 8. The surface tension of a liquid, (a) increases with area, (b) decreases with, area, (c) increases with temperature, (d) decreases with temperature, , 4. Hairs of shaving brush cling together when it is, removed from water due to, (a)Force of attraction between hair, (b)surface tension, (c)viscosity of, water (d)characteristic property of hairs, , 9., , 5. In the glass capillary tube, the shape of the, surface, of the liquid depends upon, , 10., , Mercury does not wet glass , wood or iron, because, (a) cohesive force is less than adhesive force, (b) cohesive force is greater than adhesive force, (c) angle of contact is less than 90 (d)cohesive, force is equal to adhesive force, The surface tension of rain water is 72 x 103, N/m. If the diameter of a drop of rain is 2 x

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11., , 12., , 104 m, the difference between the pressures, inside and outside the drop is, (a) 72 N/m², (b)144 N/m², (c)14.0 N/m², (d)1440N/m², The pressure inside a spherical drop of water is, equal to 2 atmospheres. The pressure outside is, 1 atmosphere. If the surface tension of water is, 74 x 103 N/m, the diameter of the bubble is, (a) 0.003 mm, (b) 0.06 mm, (c) 0.5 mm, (d) 0.05 mm, A soap bubble 2 cm in diameter is formed on a, pipe attached to a water manometer. The, differential pressure is observed as 1.20 mm of, water. The surface tension of the soap solution, is, (a) 0.030 N/m, (b) 0.060 N/m, (c) 0.015 N/m, (d) 0.070 N/m, , 13. Excess pressure of one soap bubbles is four, times more than the other. then the ratio of, volume of first bubble to another one is, (a)1:64, (b)1:4, (c)64:1, (d)1:2, 14. Two long capillary tubes A and B of radius, RB>RA, dipped in same liquid . Then, (a) Water rise is move in A than B, (b) Water rise is move in B than A, (c) Same water rise in both, (d) All of these according to the density of, water, 15. Water rise up to a height h in a capillary tube of, certain diameter. This capillary tube is, replaced by, a Similar tube of half the diameter. Now the, water, will rise to the height of, (a) 4h, (b) 3h, (c) 2h, (d) h, 16. If a glass rod is dipped in mercury and with, drawn, out, the mercury does not wet the rod because, (a) angle of contact is acute, (b) cohesion force is more, (c) adhesion force is more, (d) density of mercury is more, 17. Water rises in a capillary tube to a certain height, such that the upward force tension is balanced, by 75 x10-4N force due to the weight of the, liquid. if the surface tension of water is 6 x102, Nm-1, the inner circumference of the capillary, must be, (a) 1.25 x10-2m, (b) 0.50 x10-2m, -2, (c) 6.5 x10 m, (d)12.5 x10-2m, , 18. If the diameter of a capillary tube is doubled ,, then the height of the liquid that will rise is, (a) twice (b) half (c) same as earlier (d) none of, these, 19., , A capillary tube of bore 0.5 mm stands, vertically in a wide vessel containing a liquid, whose surface tension is 30x103. The liquid, wets the tube and has a specific gravity of 0.8., The rise of liquid in the tube is (take  = 0), (a) 0.03 m(b) 0.30 m (c) 0.06 m (d) 0.001 m, , 20., , Three surfaces of liquids are shown here. Find, the correct statement:, , [A], [B], [C], (a) the surface tension of liquid A is infinite and, such a surface is not possible practically, (b) in case of liquid B, the resultant force on a, molecule on the surface would be downward,, and the surface is concave., (c) In case of liquid C, the resultant force due to, surface tension is direction downwards, (d) the surfaces of all three liquids A, B and C are in, equilibrium and so the net force due to surface, tension is the same., 21., , A mercury barometer tube is 0.003 m in, diameter. If the surface tension of mercury is, 465x103 N/m and the contact angle is 128°,, the error introduced in the reading due to, surface tension is, (a) 0.0014 m, (b) 0.0021 m, (c) 0.0028 m, (d) 0.0012 m, 22. The surface tension of a liquid is 5N/m. if a thin, film of the area 0.02m2is formed on a loop., then its energy will be, (a)5 x102j (b)2.5 x10-2j (c)2 x10-1j (d)5 x-1j, 23. Radius of a soap bubble is r, surface tension of, soap solution is T. then without increasing the, temperature, how much energy will be needed, to double its radius, (a)4⊼r2t, (b)2⊼r2t (c)12⊼r2t, (d)24⊼r2t, 24. The work done in blowing a soap bubble of, radius r and surface tension  is, (a) 2r² (b) 4r² (c) 16r², (d) 8r², 25. Two droplets merge with each other and forms a, large droplet. in this process, (a) energy is liberated (b) energy is absorbed, (c) neither liberated nor absorbed, (d) some mass is converted into energy

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26., , 27., , 28., , Air is pushed into a soap bubble of radius R,, until this radius is doubled. If the surface, tension of the soap solution is , the work, done in the process is, (a) 8R² (b) 4R² (c) 16R² (d) 24R², A soap film is formed on a wire frame with, L, horizontal wire AB free, P, Q, to move up and down., The wire AB is pulled, down to a position AB, by a distance x. If  is A, B, the surface tension of the A, B, soap solution, the work, F, done is, (a) Lx, (b) 2 Lx (c) x, (d) 2x, The work done in blowing a soap bubble of, radius 0.1 m (the surface tension of the soap, solution is, 30 x 103 N/m) is, (a) 7.5 x 104 J, (b) 15 x 104 J, 4, (c) 75 x 10 J, (d) 75 x 103 J, , 35., , smaller bubble till the sizes become equal, (d) there is no flow of air., A capillary tube (A) is dipped in water., Another identical tube (B) is dipped in a soapwater solution. Which of the following shows, the relative nature of the liquid columns in the, two tubes?, A, , (a), A, , (b) 4/3⊼(r3n-r2), , (c) 4⊼T (r2-nr2), , (d) 4⊼T(nr2 +R2), , 30. A spherical liquid drop of radius R is divided, into eight equal droplets. if surface tension is, T, then the work done in this process will be, (a)2⊼R2t (b)3⊼R2t (c)4⊼R2t, (d)2⊼Rt2, 31. The surface tension of liquid is 0.5N/m. if a film, is, held on a ring of area 0.02m2, its surface energy, is, (a)5 x 10-2joule, (b)2.0 x10-2joule, -4, (c)4 x10 joule, (d)0.8 x10-1 joule, 32. What is ratio of surface energy of 1 small drop, and 1large drop. if 1000 small drops, combined to form 1 large drop, (a)100:1, (b)1000:1, (c)10:1, (d)1:100, 33. Radius of a soap bubble is increased from r to 2r, work done in this process in terms of surface, tension is, (a)24⊼r2s (b)48⊼r2s (c)12⊼r2s (d)36⊼r2s, 34. If two soap bubbles of different radii are, connected by a tube,, (a) air flows from the smaller bubble to the, bigger., (b) air flows from bigger bubble to the smaller, bubble till the sizes are interchanged, (c) air flows from the bigger bubble to the, , B, , (b), A, B, , (c), , 29. Energy needed in breaking a drop of radius R, into n, drops of radii r is given by, (a) 4⊼T(nr2 –R2), , B, , A, , B, , (d), ...By Praveen Gupta