Tiêu đề 5--advanced-problem-package-liquids-.pdf ✅

Liquids 1. A vessel of uniform cross section (open at the top with an orifice at the bottom contains oil (relative density 0.8 ) on top of water. Water flows out of the vessel. The initial speed of water for the values given in the figure is nearly. (Take g = 10 m/s 2 (A) 10.0 m/s (B) 8.0 m/s (C) 16.7 m/s (D) 5.0 m/s 2. Two communicating vessels contain mercury. The diameter of one vessel is n times than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel ( s = relative density of mercury and ρ = density of water) by (A) n 2h (n+1) 2s (B) h (n2+1)s (C) h (n+1) 2s (D) h n2s 3. Three liquids having densities ρ1, ρ2 and ρ3 are filled in a U-tube. Length of each liquid column is equal to l, ρ1 > ρ2 > ρ3 and liquids remain at rest (relative to the tube) in the position shown in the figure. It is possible that : (A) U-tube is accelerating leftwards (B) U-tube is accelerating upwards with acceleration g (C) U-tube is moving with a constant velocity (D) None of the above 4. A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be : (A) 7 1/3 2 (B) 5 1/3 2 (C) 9 1/3 2 (D) 3 1/3 2 5. In the figure shown the velocity and pressure of the liquid at the small cross section (2) are given by : (If P0 is the atmospheric pressure). (A) √2hg,P0 + ρhg 2 (B) √hg,P0 + ρhg 2 (C) √ hg 2 , P0 + 3ρhg 4 (D) √hg 2 , P0 + 3ρhg 4 6. A cubic block of side a is connected with two similar vertical springs as shown. Initially, bottom surface of the block of density σ touches the surface
of the fluid of density 2σ while floating. A weight is placed on the block so that it is immersed half the fluid, then the weight is : (A) a ( K 2 + a 2σg) (B) a(K + a 2σg) (C) a (K + a 2 2 σg) (D) a 2 (K + a 2σg) 7. A hollow sphere of mass M and radius R is immersed in a tank of water (density ρw ). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle 45∘ with the horizontal as shown in the figure. The tension T1 in the wire is: (A) 4 3 πR 3ρwg−Mg √2 (B) 2 3 πR 3ρwg − Mg (C) 4 3 πR 3ρwg − Mg (D) 4 3 πR 3ρwg + Mg 8. A body of density ρ ′ is dropped from rest at a height h into a lake of density ρ where ρ > ρ. Neglecting all dissipative forces calculate the maximum depth to which the body sinks before returning to float on the surface. (A) h ρ−ρ′ (B) hρ ′ ρ (C) hρ ′ ρ−ρ′ (D) hρ ρ−ρ′ 9. 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 ω. The force exerted by the liquid at the other end is : (A) Mω 2 L/2 (B) Mω 2 L (C) Mω 2 L/4 (D) Mω 2 L 2 /2 10. A solid sphere of radius r is floating at the interface at the interface of two immiscible liquids of densities ρ1 and ρ2 (ρ2 > ρ1 ), half of its volume lying in each. The height of the upper liquid column from the interface of the two liquids is h. The force exerted on the sphere by the upper liquid is (atmoshperic pressure = p0 and acceleration due to gravity is g ): (A) P0πr 2 + (h − 2 3 r) πr 2ρ1g (B) (h − 2 3 r) πr 2ρ1g (C) 2 3 πr 3ρ1g (D) P0 × πr 2 11. A cylinderical wooden float whose base area S and the height H drifts on the water surface. Density of wood d and density of water is ρ. What minimum work must be performed to take the float out of the water? (A) Sdg 2H2 4ρ (B) Sg d 2H2 2ρ (C) Sg d 2H2 ρ (D) Sg d 2H2 3ρ
12. Figure shows a metal ball suspended by thread of neglible mass from an upright cylinder that floats partially submerged in water. The cylinder has height 6 cm, face area 11 cm2 on the top and bottom and density 0.5 g/cm3 . 4 cm of cylinder's height is inside the water surface. If density of the metal ball is 8gm/cm3 then its radius is equal to: (ρw = 1gm/cm3 ) (A) ( 3 8 ) 1/3 cm (B) ( 3 4 ) 1/3 cm (C) ( 6 8 ) 1/3 cm (D) ( 5 11) 1/3 cm 13. An isolated and charged spherical soap bubble has a radius ' r ' and the pressure inside is atmospheric. If ' T ' is the surface tension of soap solution, then charge on drop is: (A) 2√ 2rT ε0 (B) 8πr√2rTε0 (C) 8πr√rTε0 (D) 8πr√ 2rT ε0 14. Consider a small water drop in air. If T is the surface tension, then what is the force due to surface tension acting on the smaller section ABC ? (A) 2πTR (B) 2πTRsin θ (C) 2πTRsin2 θ (D) 2πTRsin3 θ 15. In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction μ = Sh V . A very small hole of area S is made at depth ' h '. Water of volume ' V ' is filled in the container. The friction is not sufficent to keep the container at rest. The acceleration of the container initially is: (A) V Sh g (B) g (C) zero (D) Sh V g MULTIPLE CORRECT ANSWERS TYPE Each of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. Figure shows a container filled with a liquid of density ρ. Four points A, B, C and D on the vertices of a vertical square. Points A and C lie on a vertical line and points B and D lies on a horizontal line. Choose the correct statement(s) about the pressure at the four points. (A) PD = PB (B) PA < PB = PD < PC (C) PD = PB = PC−PA 2 (D) PD = PB = PC+PA 2
17. A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross section A1 and A2 are v1 and v2 respectively. The difference in the levels of the liquid in the two vertical tubes is h. Then (A) The volume of the liquid flowing through the tube in unit time is A1v1 (B) v2 − v1 = √2gh (C) v2 2 − v1 2 = 2gh (D) The energy per unit mass of the liquid is the same in both sections of the tube 18. A rectangular vessel of dimension (l × b × h) and mass M contains a liquid of density ρ. The vessel has an orifice at its bottom at a distance c from the rear wall as shown in the figure. (A) The maximum volume of the water that can be stored when the vessel is accelerated is hcb/2 (B) The maximum volume of the water that can be stored when the vessel is accelerated is hlb/2 (C) Force F that must be applied when maximum water stored is [M + hcbρ 2 ] hg c (D) Force F that must be applied when maximum water stored is [M + hcbρ 2 ] lg c 19. A wooden block is floating in a water tank. The block is pressed to the bottom. During the process, a work is done. Which of the following statements are false? (A) Work done is equal to work done against upthrust exerted by the water (B) Work done is equal to work done against upthrust plus loss of gravitational potential energy of the block (C) Work done is equal to work done against upthrust minus loss of gravitational potential energy of the block (D) Work done is equal to loss of gravitational potential energy of the block 20. The mass of block is m1 and that of liquid with the vessel is m2. The block is suspended by a string (tension T) partially in the liquid. The reading of the weighting machine placed below the vessel. (A) is (m1 + m2 )g (B) is greater than (m1 + m2 )g (C) is equal to (m1g + m2g − T) (D) is less than (m1 + m2 )g 21. A body floats on water and also on an oil of density 1.25 . Which of te following is/are true? (A) The body loses more weight in oil than in water (B) The volume of water displaced is 1.25 times that of oil displaced. (C) The body experiences equal upthrust from water and oil (D) To make the body just sink, one will need 1.25 times load in case of oil than in case of water 22. Each of the following system begins moving upwards with a constant acceleration. Select these cases in which quanity will change due to this upward acceleration : (A) time period of simple pendulum (B) fraction of floating body submerged in a liquid (C) tiem period of a spring block system (D) pressure on the base of a container containing liquid 23. Two tubes of uniform cross-section are held vertically. uA and uB are the velocities of fluid flow at A and B respectively, and pA and pB are pressure at A and B respectively. Arrow B show the direction of fluid flow.