02 - Elasticity, Fluid Dynamics (Complete)Ex. . Module-2pdf

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LEVEL # 1 Q.1 (a) Glass is more elastic than rubber (b) Rubber is more elastic than glass (c) Steel is more elastic than rubber (d) Rubber is more elastic than steel For the above statements– (A) (a) and (b) are correct (B) (a) and (c) are correct (C) (b) and (c) are correct (D) (b) and (d) are correct Q.2 Two similar balls, one of which is made of ivory while the other, of clay, are dropped from the same height, then– (A) the ivory ball will bounce to a greater height (B) the caly ball will bounce to a greater height (C) both the balls will bounce to the same height (D) the ivory ball will not at all bounce Q.3 Which of the following is not dimension less– Q.7 On withdrawing the applied force on some objects, the deformity caused gradually diminishes with time. This is called– (A) elastic fatigue (B) elastic limit (C) coefficient of elasticity (D) elastic after effect Q.8 On stretching some substances, permanent elongation is caused, because– (A) they are perfectly elastic (B) they are perfectly plastic (C) more stress acts on them (D) their strain is infinite Q.9 Out of the following whose elasticity is independent of temperature– (A) steel (B) copper (C) invar steel (D) glass Q.10 A cable that can support a load W is cut into two equal parts. The maximum load that can be supported by either part is– (A) Poisson ratio (B) Sharing strain (C) Longitudinal strain (D) Volume stress (A) W 4 (B) W 2 Q.4 The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of– (A) thin block of any cross section (B) thick block of any cross section (C) long thin wire (D) short thin wire Q.5 The modulus of elasticity of a material does not depend upon– (A) shape (B) temperature (C) nature of material (D) impurities mixed Q.6 A steel wire is stretched by 1 kg. wt. If the radius of the wire is doubled, its Young’s modulus will– (A) remain unchanged (B) become half (C) become double (D) become four times (C) W (D) 2 W Q.11 On withdrawing the external applied force on bodies within the elastic limit, the body– (A) regains its previous state very quickly (B) regains its previous state after some time (C) regain its previous state after a very long time (D) does not regain its previous state Q.12 Elasticity is the property which is caused by– (A) the applied deforming forces (B) gravitational force (C) nuclear forces (D) inter-molecular forces Q.13 The effect of temperature on the value of Young’s modulus of elasticity for various substances in general is– (A) it increases with increase in temperature (B) remains constant (C) decrease with rise in temperature (D) sometimes increases and sometimes decreases with temperature Q.14 The number of independent elastic constants of a solid is– (A) 1 (B) 2 (C) 3 (D) 4 Q.15 The ratio of coefficient of isothermal and adiabatic elasticities of a gas is– (A)  (B) 2 (C) 1/ (D) 1/2 Q.22 The ‘

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02 - Elasticity, Fluid Dynamics (Complete)Ex. . Module-2pdf

• 1. Elasticity &Fluid dynamics Total No.of questions in Elasticity & Fluid dynamics are - Level # 1 ....................................................................................41 Level # 2 ....................................................................................32 Level # 3 ....................................................................................14 Level # 4 ....................................................................................23 Total No. of questions ............................................................ 110
• 2. Q.1 (a) Glass is more elastic than rubber (b) Rubber is more elastic than glass (c) Steel is more elastic than rubber (d) Rubber is more elastic than steel For the above statements– (A) (a) and (b) are correct (B) (a) and (c) are correct (C) (b) and (c) are correct (D) (b) and (d) are correct Q.2 Two similar balls, one of which is made of ivory while the other, of clay, are dropped from the same height, then– (A) the ivory ball will bounce to a greater height (B) the caly ball will bounce to a greater height (C) both the balls will bounce to the same height (D) the ivory ball will not at all bounce Q.3 Which of the following is not dimension less– (A) Poisson ratio (B) Sharing strain (C) Longitudinal strain (D) Volume stress Q.4 The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of– (A) thin block of any cross section (B) thick block of any cross section (C) long thin wire (D) short thin wire Q.5 The modulus of elasticity of a material does not depend upon– (A) shape (B) temperature (C) nature of material (D) impurities mixed Q.6 A steel wire is stretched by 1 kg. wt. If the radius of the wire is doubled, its Young’s modulus will– (A) remain unchanged (B) become half (C) become double (D) become four times Q.7 On withdrawing the applied force on some objects, the deformity caused gradually diminishes with time. This is called– (A) elastic fatigue (B) elastic limit (C) coefficient of elasticity (D) elastic after effect Q.8 On stretching some substances, permanent elongation is caused, because– (A) they are perfectly elastic (B) they are perfectly plastic (C) more stress acts on them (D) their strain is infinite Q.9 Out of the following whose elasticity is independent of temperature– (A) steel (B) copper (C) invar steel (D) glass Q.10 A cable that can support a load W is cut into two equal parts. The maximum load that can be supported by either part is– (A) 4 W (B) 2 W (C) W (D) 2 W Q.11 On withdrawing the external applied force on bodies within the elastic limit, the body– (A) regains its previous state very quickly (B) regains its previous state after some time (C) regain its previous state after a very long time (D) does not regain its previous state Q.12 Elasticity is the property which is caused by– (A) the applied deforming forces (B) gravitational force (C) nuclear forces (D) inter-molecular forces Q.13 The effect of temperature on the value of Young’s modulus of elasticity for various substances in general is– (A) it increases with increase in temperature (B) remains constant (C) decrease with rise in temperature (D) sometimes increases and sometimes decreases with temperature LEVEL # 1 ELASTICITY
• 3. Q.14 The number of independent elastic constants of a solid is– (A) 1 (B) 2 (C) 3 (D) 4 Q.15 The ratio of coefficient of isothermal and adiabatic elasticities of a gas is– (A)  (B) 2 (C) 1/ (D) 1/2 Q.16 The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied– (A) length 50 cm and diameter 0.5 mm (B) length 100 cm and diameter 1 mm (C) length 100 cm and diameter 2 mm (D) length 300 cm and diameter 3 mm Q.17 An iron rod of length  and of cross-section area A is heated from 0ºC to 100ºC. If the rod neither expands nor bends, then the developed F is proportional to– (A)  (B) 0 (C) –1 (D) A–1 Q.18 When a wire is stretched, an amount of work is done. What is the amount of work done in stretching a wire through 0.1 mm, if its length is 2m and area of cross-section, 10–6m2 (Y = 2 × 1011 N/m2) (A) 5 × 10–1 J (B) 5 × 10–2 J (C) 5 × 10–3 J (D) 5 × 10–4 J Q.19 How many times is the adiabatic modulus of elasticity of gas as compared to its isothermal modulus of elasticity– (A) two times (B) three times (C)  times (D) 1/ times Q.20 An iron bar of length  cm and cross section A cm2 is pulled by a force of F dynes from ends so as to produce an elongation  cm. Which of the following statement is correct– (A) elongation is inversely proportional to length (B) elongation is directly proportional to cross section A (C) elongation is inversely proportional to A (D) elongation is directly proportional to Young’s modulus Q.21 On abruptly withdrawing the stretching force acting on a wire, its temperature will– (A) increase (B) decrease (C) remain unchanged (D) nothing can be stated Q.22 The ‘’ of a material is 0.20. If a longitudinal strain of 4.0 × 10–3 is caused, by what percentage will the volume change– (A) 0.48 % (B) 0.32 % (C) 0.24 % (D) 0.50 % Q.23 A cylinder is of length  and diameter d. On stretching the cylinder, an increment  in length and decrease d in diameter are caused. The Poisson ratio is– (A)  = d d       (B)  =       d d (C)  = d d       (D)  = d d       Q.24 Steel is more elastic than rubber because for a given load the strain produced in steel as compared to that produced in rubber is– (A) more (B) less (C) equal (D) nothing can be said Q.25 In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain  and modulus of elasticity Y is– (A) Y 2/2 (B) Y /2 (C) Y 2 (D) Y2 /2 Q.26 The formula for compressibility of a gas is– (A) PdV/V (B) (1/P) dP/dV (C) V . dV dP (D) dP dV . V 1 Q.27 The potential energy of a metallic rod when it is compressed– (A) increases (B) remains constant (C) decreases (D) becomes infinite FLUID DYNAMICS : BERNOULLI'S THEORY & EQUATION OF CONTNUITY Q.28 An incompressible fluid flows steabily through a cylindrical pipe which has radius 2R at point A and radius R at point B further along the flow direction. If the velocity at point A is , its velocity at point B will be – (A) 2 (B)  (C) /2 (D) 4 Q.29 Water is flowing in a horizontal pipe of non- uniform cross - section. At the most contracted place of the pipe – (A) Velocity of water will be maximum and pressure minimum (B) Pressure of water will be maximum and velocity minimum (C) Both pressure and velocity of water will be maximum (D) Both pressure and velocity of water will be minimum
• 4. Q.30 Water is flowing in a tube of non-uniform radius. The ratio of the radii at entrance and exit ends of tube is 3 : 2. The ratio of the velocities of water entering in and exiting from the tube will be – (A) 8 : 27 (B) 4 : 9 (C) 1 : 1 (D) 9 : 4 Q.31 Water from a tap emerges vertically downward with an initial speed of 1.0 ms–1. The cross- section area of the tap is 10–4m2. Assumed at the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional areal of the stream 0.15 m below the tap is (g = 10 m/s2) (A) 5.0 × 10–4 m2 (B) 1.0 × 10–5 m2 (C) 5.0 × 10–5 m2 (D) 2.0 × 10–5 m2 Q.32 The velocity of a small ball of mass M and density d1, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d2, the viscous force acting on the ball will be – (A) 2 1 d g Md (B) g ) d d ( M 2 1  (C)          1 2 d d 1 Mg (D) M d1 d2 Q.33 Bernoulli’s theorem based upon – (A) Conservation of momentum (B) Conservation of energy (C) Conservation mass (D) None of these (D) Faraday’s law Q.34 There is a gale over a house. The force on the roof of the house due to the gale is – (A) Directed downward (B) Directed upward (C) Zero (D) None of these Q.35 A tank has an orifice near its bottom. The volume of the liquid flowing per second out of the orifice does not depend upon – (A) Area of the orifice (B) Height of the liquid level above the orifice (C) Density of liquid (D) Acceleration due to gravity Q.36 The rate of flowing of water from the orifice in a wall of a tank will be more if the orific is – (A) Near the bottom (B) Near the upper end (C) Exactly in the middle (D) Does not depend upon the position of orific Q.37 A tank is filled with water to a height H. A hole is made in one of the walls at a depth D below the water surface. The distance x from the foot of the wall at which the stream of water coming out of the tank strikes the ground is given by – (A) x = 2 [D(H – D)]1/2 (B) x = 2 (gD)1/2 (C) x = 2 [D(H + D)]1/2 (D) None of these VISCOSITY Q.38 A small lead ball is falling freely in a viscous liquid. The velocity of the ball – (A) goes on increasing (B) goes on decreasing (C) remains constant (D) first increases and then becomes constant Q.39 The terminal velocity of a spherical ball of radius r falling through a viscous liquid is proportional to – (A) r (B) r2 (C) r3 (D) r –1 Q.40 The viscous force acting on a solid ball moving in air with terminal velocity  is directly proportional to– (A)  (B)  (C)  1 (D) 2 Q.41 A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by – (A) Curve A (B) Curve B (C) Curve C (D) Curve D
• 5. Q.1 A spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atmospheres. The bulk modulus of its material in dynes/ cm2 is- (A) 10 × 1012 (B) 100 × 1012 (C) 1 × 1012 (D) 2.0 × 1011 Q.2 When 1 kg wt. is suspended from a wire, the increment produced is 2 mm, What will be the increment in lengths when 4 kg wt. is suspended from it- (A) 4 mm (B) 8 mm (C) 0.5 mm (D) 10 mm Q.3 On increasing temperature, the elasticity of a material- (A) decreases (B) increases (C) sometimes increases and sometimes decreases (D) remains same Q.4 Two wires, one of copper and the other of steel, are of same length and cross section. They are welded together to from a long wire. On suspending a weight at its one end, increment in length is found to be 3 cms. If Young's modulus of steel is double that of copper, the increment in steel wire will be- (A) 1 cm (B) 2 cm (C) 1.5 cm (D) 2.5 cm Q.5 On mixing impurities, the elasticity of a material- (A) decreases (B) increases (C) sometimes increases and sometimes decreases (D) remains same Q.6 The bulk modulus of rubber is 9.1 × 108 N/ m2. To what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1%? (A) 1 km (B) 25 m (C) 100 m (D) 200 m LEVEL # 2 (ELASTICITY) Q.7 On applying the load, the increment in length of a wire is 1 mm. On applying the same load on another wire of same length and material, but having half the radius, the increment will be: (A) 0.25 mm (B) 4.0 mm (C) 0.5 mm (D) 2.0 mm Q.8 Which of the following shows greater increment in length when subjected to same load to wires made of same material : (A) L = 1 m and r = 1 mm (B) L = 1 m and r = 2 mm (C) L = 2 m and r = 1 mm (D) L = 2 m and r = 2 mm Q.9 The isothermal bulk modulus of a perfect gas at atmospheric pressure is- (A) 1.03 × 105 newton/ m2 (B) 1.03 × 104 newton/ m2 (C) 1.03 × 1010 newton/ m2 (D) 1.03 × 1011 newton/ m2 Q.10 Two rods A and B of the same material and length have their radii r1 and r2 respectively. when they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio         B of end the at twist of angle the A of end the at twist of angle the is- (A) 2 1 r / 2 2 r (B) 3 2 3 1 r / r (C) 4 1 4 2 r / r (D) 4 2 4 1 r / r Q.11 An metal rod of Young's modulus 2 × 1010 newton/ metre2, undergoes an elastic strain of 0.06%. The energy per unit volume stored in joule/metre2 is- (A) 3600 (B) 7200 (C) 1800 (D) 900 Q.12 The compressibility of water is 4 × 10–5 per unit atmospheric pressure. The decreased volume of 100 cm3 of water under a pressure of 100 atmosphere will be- (A) 0.4 cm3 (B) 4 × 10–5 cm3 (C) 0.025 m3 (D) 0.004 cm3 Q.13 The Young's modulus and strain for steel at the breaking point are 2 × 1011 N/m2 and 0.15 respectively. Hence the stress at the breaking point in newton/ m2 for steel will be- (A) 1.33 × 1011 (B) 1.33 ×1010 (C) 3 × 109 (D) 3 × 1010
• 6. Q.14 The force constant between the restoring force F and displacement x of a spring according to the graph shown will be- (A) 3 (B) 3 /2 (C) 1/2 (D) 1/ 3 Q.15 If a stretching force F1 is applied on a vertical metal wire then its length is L1 and if force F2 is applied on it then its length becomes L2. The real length of wire is- (A) 1 2 1 2 2 1 F F L F L F   (B) 1 2 2 1 1 2 F F L F L F   (C) 2 L L 2 1  (D) 2 1L L Q.16 A metal rod of length , area of cross section A, Young's modulus Y, and thermal linear coefficient of expansion  is clamped at both of its ends. If it is heated through t°C, the force acting on the rod is- (A) YAt (B) YAt (C) YAt/ (D) YAt Q.17 Poisson's ratio of a certain material is 0.2 . If a longitudinal strain of 4 × 10–3 is produced in a uniform rod or this material, the percentage change in its volume will be- (A) 0.24% (B) 0.32% (C) 0.48% (D) 0.56% Q.18 Steel ring of radius r and cross- section A is to be mounted on a wooden well. If the Young's modulus of steel is Y, then the minimum tensile force required to be developed in the ring so that it can easily get mounted on the well will be- (A) r YAR (B) R YAr (C) Ar ) r R ( Y  (D) r ) r R ( YA  Q.19 After suspending a body of mass 1 kg from a wire of negligible mass, length 1 m and radius 1 mm it is made to oscillate along the length in a vertical plane. Its frequency is found to be 100 per s. Young's modulus of elasticity of the material of wire is- (A) 1.05 × 1011 N/m2 (B) 1.26 × 1011 N/ m2 (C) 2. 12 × 1011 N/ m2 (D) 2.84 × 1011 N/m2 Q.20 On suspending a weight Mg, the length  of elastic wire and area of cross- section A, its length becomes double the initial length. The instantaneous stress action on the wire is- (A) Mg/A (B) Mg /2A (C) 2Mg/ A (D) 4 Mg/A FLOW OF FLUID & BERNOULLI'S THEORY & EQUATION OF CONTNUITY Q.21 Velocity of flow of water in a horizontal pipe is 10.0 m/s. Find the velocity- head or water (g = 10.00 m/s2) (A) 9.00 m (B) 5.00 m (C) 3.00 m (D) None of these Q.22 Water is flowing through a cylindrical pipe of cross- section area 0.09  m2 at a speed of 1.0 m/s. If the diameter of the pipe is halved, then find the speed of flow of water through it- (A) 4.0 m/s (B) 6.0 m/s2 (C) 4.0 m/s2 (D) 6.0 m/s Q.23 Water is flowing through a horizontal tube of non- uniform cross- section. At a place the radius of the tube is 0.5 cm and the velocity of water there is 20 cm/s. What will be the velocity at another place where the radius of the tube is 1.0 cm? (A) 3 cm/s (B) 7 cm/s (C) 5 cm/s (D) 0.5 cm/s Q.24 Water is flowing in a horizontal pipe of non- uniform area of cross- section. The velocity of water at a place, where the radius of pipe is 0.01 m is 25 m/s. What will be the velocity of water where the radius of pipe is 0.02 m? (A) 7.25 m/s (B) 6.75 m/s (C) 6.25 m/s (D) None of these length have their radii r1 F x 300
• 7. Q.25 Water is flowing through a horizontal pipe of non- uniform cross- section. The speed of water is 30 cm/s at a place where pressure is 10 cm(of water). Calculate the speed of water at the other place where the pressure is half of that of the first place- (A) 100.4 cm/s (B) 101.4 cm/s (C) 102.4 cm/s (D) 103.4 cm/s Q.26 Water enters a horizontal pipe of non- uniform cross-section with a velocity of 0.5 m/s and leaves the other end with a velocity of 0.7 m/s. The pressure of water at the first end is 103 N/m2. Calculate pressure at the other end. (Density of water = 1.0 × 103 kg/m3)- (A) 980 N/m2 (B) 880 N/m2 (C) 800 N/m (D) None of these Q.27 A water tank has a hole in its wall at a distance of 40 m below the free surface of water. Compute the velocity of flow of water from the hole. If the radius of the hole is 1 mm., find the rate of flow of water- (A) 26 m/s , 8.8 × 10–5 m3/s (B) 28 m/s, 8.8 × 10–5 m3/s (C) 28 m/s, 6.8 × 10–5 m3/s (D) 26 m/s, 9.8 × 10–5 m3/s Q.28 The relative velocity between two parallel layers of water is 8 cm/s and the perpendicular distance between them is 0.1 cm. Calculate the velocity- gradient- (A) 90/s (B) 80.5 /s (C) 80 /s. (D) None of these Q.29 There is a 1 mm thick layer of oil between a flat plate of area 10–2 m2 and a big plate. How much force is required to move the plate with a velocity of 1.5 cm/s2? The coefficient of viscosity of oil is 1 poise- (A) 1.5 × 10–3 N (B) 1.3 × 10–5 N (C) 1.5 × 10–2 N (D) 1.5 × 102 N Q.30 A steel shot of diameter 2 mm is dropped in a viscous liquid filled in a drum. Find the terminal speed of the shot. Density of the material of the shot = 8.0 × 103 kg/m3, density of liquid = 1.0× 103 kg/ m3. Coefficient of viscosity of liquid = 1.0 kg/(m-s), g= 10 m/s2 (A) 1.55 cm/s (B) 1.455 cm/s (C) 5.1 cm/s (D) None of these Q.31 An air bubble (radius 0.4 mm) rises up in water. If the coefficient of viscosity of water be 1 × 10–3 kg/(m–s), then determine the terminal speed of the bubble density of air is negligible- (A) 0.843 m/s (B) 3.048 m/s (C) 0.483 m/s (D) 0.348 m/s Q.32 If an oil drop of density 0.95 × 103 kg/ m3 and radius 10–4 cm is falling in air whose density is 1.3 km/m3 and coefficient of viscosity is 18 × 10–6 kg/(m–s). Calculate the terminal speed of the drop. (A) 0.00015 cm/s (B) 0.0005 cm/s (C) 0.0115 cm/s (D) None of these
• 8. LEVEL # 3 Q.1 The terminal velocity of a ball in air is v, where acceleration due to gravity is g. Now the same ball is taken in a gravity free space where all other conditions are same. The ball is now pushed at a speed vv, then – (A) The terminal velocity of the ball will be v/2 (B) The ball will move with a constant velocity (C) The initial acceleration of the ball is 2g in opposite direction of the ball's velocity (D) The ball will finally stop (Given that density of the ball  = 2 times the density of air ) Q.2 A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is – (A) H (B) 1.25 H (C) 1.5 H (D) 2H Q.3 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 – (A) h2 – h1 (B) h2 + h1 (C) 2 h h 1 2  (D) 2 h h 1 2  Q.4 Two drops of same radius are falling through air with steady speed v. If the two drops coalesce, what would be the terminal speed – (A) 4v (B) 2v (C)3v (D) None of these Q.5 A large tank is filled with water (density = 103 kg/m3). A small hole is made at a depth 10m below water surface. The range of water issuing out of the hole is R on ground. What extra pressure must be applied on the water surface so that the range becomes 2R (take 1 atm = 105 Pa and g = 10 m/s2) : (A) 9 atm (B) 4 atm (C) 5 atm (D) 3 atm Q.6 A ball of relative density 0.8 falls into water from a height of 2m. The depth to which the ball will sink is (neglect viscous forces) – (A) 8m (B) 2 m (C) 6m (D) 4 m Q.7 When tension in a metal wire is T1, its length was l1 and when tension is T2, the length is l2. Its unstretched length is – (A) 2 1l l (B) 2 2 1 l l  (C) 1 2 1 2 2 1 T T ) T T (   l l (D) 2 1 2 1 2 1 T T T T   l l Q.8 When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is : (Given Density of water = 1g/cm3) (A) 9.8 × 1010 N/m2 (B) 10.2 × 1010 N/m2 (C) 0.98 × 1010 N/m2 (D) 8.4 × 1010 N/m2
• 9. Passage # 1 Fig shows a bar of uniform cross-section of area s. Equal and opposite tensile forces are applied at the ends of the bar. Each force has a magnitude F. ABCD is a plane through the bar and inclined at angle  with the perpendicular to the length of the bar. F F D C A B  Answer the following questions : (9 to 11) Q.9 Normal stress at the plane which is inclined with the plane perpendicular to the length of the bar is - (A) F/s (B) Fcos/s (C) Fcos2/s (D) F/scos Q.10 Shear stress on the plane which is inclined with the plane perpendicular to the length of the bar is (A) Fsin/s (B) F/s cos (C) Ftan/s (D) Fsin2/2s Q.11 Shear stress on the s aid plane will be maximum for = (A) 90° (B) 45° (C) 30° (D) 0° Passage # 2 (12 to 14) A U-tube of base length L contains a liquid of density  in it. The tube is rotated about one of its vertical end with angular velocity  as shown. The diameter of the tube is negligible. Take P0 as atmospheric presure. h0 h1 h2 L A B  Answer the following questions : - Q.12 What is the force at B due to rotations of the u-tube ? (A) A 2 (B) A 2L2 (C) 2 L A 2 2  (D) 4 L A 2 2  Q.13 What is the presure at B from left hand side. (A) P0 + h1 g (B) P0 + 2 g h1  (C) 2P0 + h1 g (D) P0 + h1 g + 2 L2 2  Q.14 The value of h0 is - (A) g 2 L 2  (B) g 2 L2 2  (C) g 3 L2 2  (D) g 4 L2 2 
• 10. LEVEL # 4 [PREVIOUSLY ASKED QUESTIONS IN AIEEE & IIT] Section - A Q.1 A wire suspended vertically from one of itsends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is – (A) 10 J (B) 20 J (C) 0.1 J (D) 0.2J Q.2 A spring of spring constant 5 × 103 N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is – (A) 18.75 N-m (B) 25.00 N-m (C) 6.25 N-m (D) 12.50 N-m Q.3 A wire fixed at the upper end stretched by length  by applying a force F. The work done in stretching is – (A) 2F (B) F (C)  2 F (C) 2 F Q.4 If 'S' is stress and 'Y' is Young's modulus of material of a wire, the energy stored in the wire per unit volume is (A) 2S2Y (B) Y 2 S2 (C) 2 S Y 2 (D) Y 2 S Q.5 A wire elongates by  mm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm)– (A) zero (B) /2 (C)  (D) 2 (ELASTICITY) Q.6 Two wires are made of the same material and have the same volume. Howerver wire 1 has cross-section area A and wire 2 has cross-section area 3A. If the length of wire 1 increases by x on applying force F, how much force is needed to stretch wire 2 by the same amount ? (A) F (B) 4 F (C) 6 F (D) 9 F Section - B Q.1 A highly rigid cubical block of small mass M and side L is fixed rigidly on to another cubical block B of the same dimensions and of low modulus of rigidity  such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by - (A) 2 L M (B) 2 L / M (C) 2  / ML (D) 2 L / M  Q.2 A uniform rod of length L and density  is being pulled along a smooth floor with a horizontal acceleration (see figure). The magnitude of the stress at the transverse cross-section through the mid-point of the rod is  L (A) (1/2L) (B) (1/4L) (C) (1/8L) (D) (L)
• 11. Q.3 One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of spring. The area of cross-section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to - (A) 2 m K (B) 2 m YA KL YAK ( )  (C) 2 mYA KL (D) 2 mL YA Q.4 A weight W is suspended through a rope of length 1 m and cross-sectional area 10-6 m2 from a rigid support. The relation between change in length of rope l & W is shown in the graph. The young’s Modulus of elasticity is : (A) 2×10-5 (B) 2×1011 (C) 5×104 (D) 5×1010 (FLUID DYNAMICS) Section - A Q.1 A cylinder of height 20 m is completely filled withwater.The velocityof efflux of water(inms–1 ) through a small hole on the side wall of the cylinder near its bottom is – (A) 10 m/s (B) 20 m/s (C) 25.5 m/s (D) 5 m/s Q.2 Which one of the following representsthecorrect dimensionsof the coefficient of viscosity ? (A) ML–1 T–1 (B) MLT–1 (C) ML–1 T–2 (D) ML–2 T–2 Q.3 Spherical ballsof radius‘R’arefalling in aviscous 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’ Q.4 A 20 cm long capillary tube is dipped in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be (A) 8 cm (B) 10 cm (C) 4 cm (D) 20 cm Q.5 If the terminal speed of a sphere of gold (densit y = 19.5 kg/m3) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m3), find the terminal speed of a sphere of silver (density = 10.5 kg/m3) of the same size in the same liquid– (A) 0.1 m/s (B) 0.2 m/s ( C ) 0.4 m/s (D) 0.133 m/s Q.6 A jar is filled with two non-mixing liquids 1 and 2 having densities 1 and 2 , respectively. Asolid ball, made of a material of density 3 , isdropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following istrue for 1 , 2 and 3 ? Liquid 1   Liquid 2  (A) 1 > 3 > 2 (B) 1 <   (C) 1 <   (D) 3 <  2
• 12. Q.7 A spherical solid ball of volume V is made of a material of density 1 . It is falling through a liquid of density 2 (2 < 1 ). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed , i.e., Fviscous = – k2 (k > 0). The terminal speed of the ball is (A) k Vg 1  (B) k Vg 1  (C) k ) ( Vg 2 1    (D) k ) ( Vg 2 1    Section - B Q.1 A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is – (A) 2 L M 2  (B) M2L (C) 4 L M 2  (D) 2 L M 2 2  . Q.2 A horizontal pipeline carries water in a streamline flow. At a point along the pipe where the cross-sectional area is 10 cm2, the water velocity is 1 m s–1 and the pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area is 5 cm2 is (Density of water = 103 kg m–3) (A) 500 Pa (B) 1000 Pa (C) 250 Pa (D) 750 Pa Q.3 Water from a tap emerges downwards with an initial speed of 1.0 ms–1. The cross- sectional area of the tap is 10–4m2. Assume that the pressure is constant throughout the stream of water, and the flow is steady. the cross-section area of the steam 0.15m below the tap is : (A) 5.0 × 10–4 m2 (B) 1.0 × 10–5m2 *(C) 5.0 × 10–5 m2 (D) 2.0 × 10–5 m2 Q.4 A large open tank has two holes in the wall. One is a 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 same. Then, R is equal to - (A)  2 L (B) 2L (C) L (D)  2 L . Q.5 A vessel filled with water upto height 3m. There is a hole at height 52.5 cm from the bottom. Ratio of area of cross section of hole to vessel is 0.1. Then square of velocity of the water coming out of hole in (m/s)2 (A) 50 (B) 50.5 (C) 51 (D) 40 Q.6 STATEMENT – 1 The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. and STATEMENT – 2 In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant. (A) STATEMENT – 1 isTrue, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for STATEMENT -1 (B) STATEMENT – 1 isTrue, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1 (C) STATEMENT-1 isTrue, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True
• 13. ANSWER KEY LEVEL # 1 LEVEL # 2 Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ans. B A D C A A A B C C B D C B C A B C C C Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ans. B C B B A D C D A B C C B B C A A D B B Q.No. 41 Ans. C Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ans. C B A A C C B C A C A A D D B B A D B C Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 Ans. B A C C D B B C C A D C LEVEL # 3 Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Ans. D C D A D A C A C D B C D D LEVEL # 4 ELASTICITY SECTION-A SECTION-B Q.No. 1 2 3 4 Ans. D A B B FLUID DYNAMICS SECTION-A SECTION-B Q.No. 1 2 3 4 5 6 7 Ans. B C B D A C D Q.No. 1 2 3 4 5 6 Ans. A A C A A A Q.No. 1 2 3 4 5 6 Ans. C A D B C D
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