# . In an elevator accelerating upward (A) both the elevator accelerating upward (B) the first is equations are valid

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1 IIT JEE Achiever 2014 Ist Year Physics-2: Worksheet-1 Date: Hydrostatics 1. A liquid can easily change its shape but a solid cannot because (A) the density of a liquid is smaller than that of a solid (B) the forces between the molecules is stronger in solid that in liquids (C) the atoms combine to form bigger molecules in a solid (D) the average separation between the molecules at larger in solids Ans (B) F 2. Consider the equations P lim and P1 P2 gz. In an elevator accelerating upward s 0 S (A) both the elevator accelerating upward (B) the first is equations are valid (C) the second is valid but not the first (D) both are invalid Ans (B) 3. The three vessels shown in figure have same base area. Equal volumes of a liquid are poured in the three vessels. 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 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 Ans (D) 5. Figure shows a siphon. The liquid shown is water. The pressure difference P B P A between the points A and B is (A) 400 N m 2 (B) 3000 N m 2 (C) 1000 N m 2 (D) zero A Ans (D) 10 cm B 6. A breaker 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 Ans (B) 7. The pressure in a liquid at two points in the same horizontal plane are equal. Consider an elevator accelerating upward and a car accelerating on a horizontal road. The above statement is correct in (A) the car only (B) the elevator only (C) both of them (D) neither of them Ans (B) 1

2 8. Suppose the pressure at the surface of mercury in a barometer tube is P 1 and the pressure at the surface of mercury in the cup is P 2. (A) P 1 = 0, P 2 = atmospheric pressure (B) P 1 = atmospheric pressure (C) P 1 = P 2 = atmospheric pressure (D) P 1 = P 2 = 0 Ans (A) 9. A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be (A) zero (B) 76 cm (C) < 76 cm (D) > 76 cm 10. A barometer kept in an elevator accelerating upward reads 76 cm. The air pressure in the elevator is (A) 76 cm (B) < 76 cm (C) > 76 cm (D) zero 11. A closed cubical box completely filled with water and is accelerated horizontally towards right with an acceleration. The resultant normal force by the water on the top of the box (A) Passes through the centre of the top (B) Passes through a point to the right of the centre (C) Passes through a point to the left of the centre (D) becomes zero 12. Consider the situation of the previous problem. Let the water push the left way by a force F 1 and the right wall be a force F 2. (A) F 1 = F 2 (B) F 1 > F 2 (C) F 1 < F 2 (D) the information is insufficient to know the relation between F 1 and F 2 Ans (B) 13. The heights of mercury surfaces in the two arms of the manometer shown in figure are 2 cm and 8 cm. Atmospheric pressure = N m 2, Find (a) the pressure of the gas in the cylinder and (b) the pressure of mercury at the bottom of the U tube. Gas Ans (a) N m 2 (b) N m If water is used to construct a barometer, what would be the height of water column at standard atmospheric pressure (76 cm of mercury)? Ans 10 7 N, No 15. A uniform glass U-tube is partially filled with a liquid. Horizontal length of the tube is 1 m. Tube is accelerating horizontally with constant acceleration of 6 m s 2. The difference in the heights of the liquid in the two arms of U-tube is (A) m (B) m (C) m (D) 6 m

3 Ans (A) h 6 m s 2 1 m 16. Water stands at a depth H behind the vertical face of a dam and exerts a certain resultant horizontal force on the dam tending to slide it along its foundation. The water also exerts certain torque tending to overturn the dam about the point O. The total width of the dam is L. Determine. (a) the total horizontal force (b) the total torque about O (c) the moment and arm of the resultant horizontal force about the line through O. Ans: 1 2 glh 2, 1 6 glh 3, H 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 18. 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 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 19. A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube (A) will increase (B) will decrease (C) will remain the same (D) will become zero 20. A wooden object floats in water kept in a beaker. The object is near of the beaker. Let P 1, P 2, P 3 be the pressures at the three points A, B and C at the bottom as shown in the figure. A B C (A) P 1 = P 2 = P 3 (B) P 1 < P 2 < P 3 (C) P 1 > P 2 > P 3 (D) P 2 = P 3 P 1. Ans (A) 21. A solid floats in a liquid in a partially dipped position (A) The solid exerts a force equal to its weight on the liquid 3

4 (B) The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid. (C) The weight of the displaced liquid equals the weight of the solid (D) The weight of the dipped part of the solid is equal to the weight of the displaced liquid. Ans (A), (B), (C) 22. The weight of an empty balloon on a spring balance is W 1. The weight becomes W 2 when the balloon is filled with air. Let the weight of the air itself be w. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon (A) W 2 = W (B) W 2 = W 1 + W (C) W 2 < W 1 + W (D) W 2 > W 1 Ans (A), (C) 23. A solid is completely immersed in a liquid. The force exerted by the liquid on the solid will (A) increase if it is pushed deeper inside the liquid (B) change if its orientation is changed (C) decrease if it is taken partially out of the liquid (D) be in the vertically upward direction, (D) 24. An ornament weighing 36g in air, weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9. Ans 2.2 g 25. A cube of ice floats partly in water in K. Oil. Find the ratio of the volume of ice immersed in water to that in K. Oil, specific gravity of K. Oil is 0.8 and that of ice is.09. Ans 1: 1 K. Oil Water 26. A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3 Ans 54.8 g 27. Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water. Ans 50 g 28. A cube of wood of mass 0 5 kg and density 800 kg m 3 is fastened to the free end of a vertical spring, of spring constant k = 50 N m 1, fixed at the bottom. Now the entire system is completely submerged in water. Find (a) the elongation or compression of the spring in equilibrium (b) the time period of vertical oscillation of the block when it is slightly depressed and released. 29. A piece of wax weighs g in air. A piece of metal weighs g in water. It is tied to the wax and both together weigh g in water. What is the specific gravity of wax? Ans: A wooden plank of length 1 m with uniform cross-section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water upto a height of 0 5 m. The specific gravity of the plank is 0 5. Find the angle that the plank makes with the vertical in equilibrium position. (Exclude the case = 0 ) 4

5 Ans: = 45. h 6 m s 2 1 m 31. Two spheres one hollow and one solid of the same external radius are immersed completely inside a liquid. (A) upthrust on hollow sphere is more (B) upthrust on solid sphere is more (C) upthrust on both is same (D) cannot be said 32. A vessel containing a liquid of density is placed in a lift moving with an upward acceleration a. The hydrostatic pressure at a depth h below the free surface of the liquid is (A) h g (B) h (g + a) (C) h (g a) (D) h (g 2 + a 2 ) 1/2 33. A closed tank filled with a fluid of density is mounted on a cart which is moving with an acceleration a. If the fluid pressure at A and B are p A and p B respectively, then (A) p A = p B (B) p A = p B + l a (C) p A = p B l a (D) p A = p B + (hg + p l )a 34. An ice cube containing an air bubble floats in a glass of water. As ice melts, the water level (A) rises (B) falls (C) remains unchanged (D) uncertain 35. A raft of wood (density 600 kg/m 3 ) of mass 120 kg floats in water. How much weight can be put on the raft to make it just sink? (A) 120 kg (B) 200 kg (C) 40 kg (D) 80 kg 36. An iceberg is floating partly immersed in a sea water. The density of sea water is 1.03 g/cm 3 and that of the ice is 0.92 g/cm 3. The fraction of the total volume of the iceberg above the level of sea water is (A) 8.1% (B) 11% (C) 34% (D) 0.8% 37. A block of wood floats in water kept in a vessel with two thirds of its volume inside water. If this vessel is placed in a lift having an upward acceleration, then now the fraction of volume inside water will be (A) more than 2/3 (B) less than 2/3 (C) equal to 2/3 (D) equal to 1 5

6 38. A boy is carrying a wood block weighing 0.1 kg (density 500 kg/m 3 ) in his left-hand and a bucket party filled with water and weighing 10 kg in his right-hand. The boy drops the block in water of bucket so that the block starts floating. The load the boy is now carrying is (A) 10 kg (B) 9.8 kg (C) 10.1 kg (D) 10.2 kg 39. A body is partly floating in a liquid. The whole system falls freely under gravity. The upthrust on the body due to the liquid is (A) zero (B) equal to weight of liquid displaced (C) equal to weight of the body in air (D) equal to weight of the immersed portion of the body 40. A balloon filled with air is weighted so that it barely floats on water. When it is pushed down so that it gets submerged a short distance in water then the balloon will (A) come up again to its former position (B) remain in the position where it is left (C) sink to the bottom (D) emerge on the liquid 41. A piece of cork (sp. Gravity 0.25) and a metallic piece (sp. Gravity = 8) are bound together. If the combination neither floats nor sinks in alcohol (sp. Gravity = 0.8), calculate the ratio of masses of cork and metal. (A) 9/22 (B) 9/11 (C) 6/11 (D) 6/ A solid uniform ball floats on the interface of two immiscible liquids. The specific gravity of the upper liquid is and that of lower one is. If the fraction of volume of the ball in the upper liquid is one- 1 2 fourth of its total volume. What is the density of the material of the ball? (A) (B) (C) (D) Find the pressure on a fish at a depth of 1 km in sea water of RD = 1, g = 10 m s -2 ). (A) 10 Pa (B) 10 3 Pa (C) 10 5 Pa (D) 10 7 Pa 44. A hollow right circular cone of base radius 10 cm and height 15 cm is completely filled with water. Find (A) weight of water (take g = 10 m s -2 ) (A) 15.5 N (B) 46.5 N (C) 155 N (D) 465 N 45. A force of 20kg-wt is applied to the smaller piston of a hydraulic press. Neglecting friction, find the force exerted on the larger piston. The diameters of the pistons are 5 cm and 25 cm respectively. (take 1 kg wt = 10 N) (A) 500 kg wt (B) 1000 kg wt (C) 1500 kg wt (D) 2000 kg wt 46. A hollow spherical ball, whose internal and external diameters are 8 cm and 10 cm is found just to float in a liquid of sp. Gravity 1.5. What is the sp. gravity of the material of the ball? (A) 2.35 (B) 3.07 (C) 5.15 (D)

7 47. A piece of iron weighing 272 g floats on mercury of sp. gravity 13.6 with 5/8 th of the volume immersed. Determine the volume and density of iron. (A) m 3 ; 6500 kg / m 3 (B) m 3 ; 8500 kg / m 3 (C) m 3 ; 8500 kg / m 3 (D) m 3 ; 6500 kg / m Calculate the mass of lead which will be required to just submerge in water a block of wood weighing 50 gram (A) when lead is attached underneath, (B) when lead is placed on the top of the block. Take sp. gravity of lead = 11.3 and of wood = (A) g; g (B) g; g (C) 9.14 g; 8.34 g (D) 8.34 g; 9.14 g 49. Two liquids of relative densities 2 and 3 are mixed together. Their volumes are in the ratio 4:9. What is the effective density of the mixture? (1) (35/13) times density of water (B) (35/13) (C) (16/7) times density of water (D) (16/11) 50. The height of mercury barometer is h when the atmospheric pressure is 10 5 Pa, The pressure at X in the shown diagram is (A) 10 5 Pa (C) Pa (B) Pa (D) Pa 51. A body floats in water with its one-third volume above the surface. The same body floats in a liquid with one third volume immersed. The density of the liquid is (A) 9 times more than that of water (B) 2 times more than that of water (C) 3 times more than that of water (D) 1.5 times more than that of water 52. A piece of ice is floating in a beaker containing thick sugar solution of water. As the ice melts, the total level of the liquid. (A) increases (B) decreases (C) remains unchanged (D) insufficient data 53. A body floats in completely immersed condition in water as shown in figure. As the whole system is allowed to slide down freely along the inclined surface, the magnitude of buoyant force 7

8 (A) remains unchanged (B) increases (C) decreases (D) becomes zero 54. The figure represents a U-tube of uniform cross-section filled with two immiscible liquids. One is water with density and the other liquid is of density. The liquid interface lies 2cm above the base. The w relation between and w is (A) = w (B) =1.02 w (C) =1.2 w (D) None of the above 55. A boat floating in a water tank is carrying a number of stones. If the stones were unloaded into water. What will happen to the water level? (A) Rises (B) Falls (C) Remains same (D) depends on number of stones and their density 56. An iron casting containing a number of cavities weighs 6000 N in air and 4000 N in water. What is the volume of the cavities in the casting? (g = 10 m s 2, relative density of iron = 8). (A) m 3 (B) m 3 (C) m 3 (D) m A 1 kg plastic ball is held stationary inside water contained in a tank, by tying it to a thread. The other end of the thread is tied to the bottom of the tank. The relative density of the material of the toy is 0.5. What is the tension in the thread? (g = 10 m s 2 ). (A) 5 N (B) 10 N (C) 15 N (D) 20 N 58. A spherical ball of radius 3.0 x 10 4 m and density 10 4 kg/m 3 falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. Viscosity of water is 9.8 x 10 6 N-s/m 2. (A) m (B) m (C) m (D) m 8

9 59. For the arrangement shown in the figure, what is the density of oil? (A) 916 kg/m 3 (B) 844 kg/m 3 (C) 512 kg/m 3 (D) 720 kg/m A solid floats in a liquid of different material. Carry out an analysis to see whether the level of liquid in the container will rise or fall when the solid melts. Take density of liquid formed by melting of solid as, and that of parent liquid as. Identify true statements. 1 (A) If (C) If 1 = 1 > C, D 2 2 2, level may rise or fall (B) If, level will fall (D) If 1 = 1 < 2 2, level will not rise, level will rise 60. An iron casting containing a number of cavities weighs 6000 N in air and 4000 N in water. What is the volume of the cavities in the casting? Density of iron is 7.87 g/cm 3. Take g = 9.8 m/s 2 and density of water = 10 3 kg/m 3 (A) 0.3 m 3 (B) 0.24 m 3 (C) 0.18 m 3 (D) 0.12 m A boat floating in a water tank is carrying a number of stones. If the stones were unloaded into water, what will happen to the water level? (A) Water level remains same (B) Water level comes down (C) Water level rises (D) Cannot say 62. A block of material has a density 1 and floats three-fourth submerged in a liquid of unknown density. Find the relation between 2 and 1? (A) 1 (B) 2 (C) (D) A metal ball weighs N. When suspended in water it has an apparent weight of N. Find the density of the metal. (A) 3840 kg/m 3 (B) 1240 kg/m 3 (C) 4312 kg/m 3 (D) 6580 kg/m A block of wood has a mass of 25 g. When a 5 g metal piece with a volume of 2 cm 3 is attached to the bottom of the block, the wood barely floats in water. What is the volume V of the wood? (A) 28 cm 3 (B) 140 cm 3 (C) 56 cm 3 (D) 100 cm 3 9

10 65. A block of wood weighing 71.2 N and of specific gravity 0.75 is tied by a string to the bottom of a tank of water in order to have the block totally immersed. What is the tension in the string? (A) 230 N (B) 66.4 N (C) 23.7 N (D) N 66. What is the minimum volume of a block of wood (density = 850 kg/m 3 ) if it is to hold a 50 kg woman entirely above the water when she stands on it? (A) 1 m 3 (B) 1.5 m 3 (C) 1.25 m 3 (D) 0.33 m An irregular piece of metal weighs g in air and 8.00 g when submerged in water. Find the volume of the metal and its density. (A) m 3, 5000 kg/m 3 (B) m 3, 2500 kg/m 3 (C) m 3, 3250 kg/m 3 (D) m 3, 3000 kg/m An irregular piece of metal weighs g in air and 8.00 g when submerged in water. If the same piece of metal weighs 8.50 g when immersed in a particular oil, what is the density of the oil? (A) 250 kg/m 3 (B) 500 kg/m 3 (C) 750 kg/m 3 (D) 1250 kg/m A beaker when partly filled with water has total mass g. If a piece of metal with density 3.00 g/cm 3 and volume 1.00 cm 3 is suspended by a thin string, so that it is submerged in the water but does not rest on the bottom of the beaker, how much does the beaker then appear to weigh if it is resting on a scale? (A) 20.6 N (B) N (C) 2.06 N (D) N 70. A tank contains water on top of mercury. A cube of iron, 60 mm along each edge, is sitting upright in equilibrium in the liquids. Find how much of it is in each liquid. The densities of iron and mercury are 7.7 x 10 3 kg/m 3 and 13.6 x 10 3 kg/m 3 respectively. (A) 28 mm in mercury and 32 mm in water (B) 32 mm in mercury and 28 mm in water (C) 16 mm in mercury and 28 mm in water (D) 28 mm in mercury and 16 mm in water 71. A small block of wood, of density 0.4 x 10 3 kg/m 3, is submerged in water at a depth of 2.9 m. Find: (a) the acceleration of the block toward the surface when the block is released and 10

11 (b) the time for the block to reach the surface. Ignore viscosity. (A) 14.7 m/s 2, 0.63 s (C) 26.8 m/s 2, 1.26 s (B) 4.9 m/s 2, 0.48 s (D) 3.29 m/s 2, 0.43 s 72. A uniform rod AB, 4 m long and weighing 12 kg, is supported at end A, with a 6 kg lead weight at B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total volume of the rod. (A) 14.2 N; m 3 (B) 19.6 N; m 3 (C) 22.7 N; m 3 (D) 9.2 N; m A solid sphere of mass m = 2kg and density = 500 kg/m 3 is held stationary relative to a tank filled with water. The tank is accelerating upward with acceleration 2 m/s 2. Calculate tension in the thread connected between the sphere and the bottom of the tank. [Density of water = 1000 kg/m 3, g = 10 m/s 2 ] (A) 148 N (B) 128 N (C) 24 N (D) 28 N 74. A solid sphere of mass m = 2kg and density = 500 kg/m 3 is held stationary relative to a tank filled with water. The tank is accelerating upward with acceleration 2 m/s 2. If the thread snaps, calculate the acceleration of sphere with respect to the tank. [Density of water = 1000 kg/m 3, g = 10 m/s 2 11

12 (A) 1 m/s 2 (B) 1.8 m/s 2 (C) 8 m/s 2 (D) 12 m/s The pressure gauge shown in figure has a spring for which k = 60 N/m and the area of the piston is 0.50 cm 2. Its right end is connected to a closed container of gas at a gauge pressure of 30 kpa. How far will the spring be compressed if the region containing the spring is (a) in vacuum and (B) open to the atmosphere? Atmospheric pressure is 101 kpa. (A) 10.9 cm; 2.5 cm (C) 1.8 cm; 1.2 cm (B) 2.5 cm; 10.9 cm (D) 1.2 cm; 1.8 cm 76. A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15.0 cm Calculate the vertical distance h from the top of the mercury in the right hand arm of the tube to the top of the water in the left-hand arm. (A) 13.9 cm (B) 18.7 cm (C) 14.7 cm (D) 12.8 cm 77. 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 with h 2 = 1.0 cm, determine the value of h 1. 12

13 (A) 2.6 cm (B) 4.3 cm (C) 10.5 cm (D) 12.6 cm 78. A wooden plank 1 m long and 0.5 m wide is floating in fresh water (density = 1000 kg m 3 ). When a boy climbs aboard, it sinks 4 cm. What is the mass of the boy? (A) 10 kg (B) 15 kg (C) 20 kg (D) 25 kg 79. Identify statements that are true I. The wall of a dam is vertical. Then the direction of force applied by water on the wall can be perpendicular at some points and can be not perpendicular at some other points. II. Force applied by water on the wall of a dam is maximum at a point h/2 from the surface where h is the height of water. III. Atmospheric pressure increases with altitude because height increases. IV. In a manometer, if liquid in arm A is at a lower height than that in arm B (exposed to air), then that means atmospheric pressure is less than the pressure inside the chamber connected to arm A. V. Two balls of the same radius one hollow and another solid are dipped completely inside water without touching side walls or bottom of container. Then, they experience same upthrust. (A) II, III only (B) II, IV, V only (C) I, II, IV only (D) IV, V only 13

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