Title 11. Fluid mechanics Easy.pdf ✅

1. If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake (a.) 10 m (c.) 20 m (c.) 60 m (d.) 30 m 2. Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g / cm3 . If the mass of the other is 48 g, its density in g / cm3 is (a.) 3 4 (c.) 2 3 (c.) 3 (d.) 5 3. An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm3 ) (a.) 350 cm3 (c.) 300 cm3 (c.) 250 cm3 (d.) 22 cm3 4. A uniformly tapering vessel is filled with a liquid of density 900 kg/m3 . The force that acts on the base of the vessel due to the liquid is ( 10 ) −2 g = ms (a.) 3.6 N (c.) 7.2 N (c.) 9.0 N (d.) 14.4 N 5. A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be (a.) 105 N/m (c.) 2 × 105 N/m (c.) Zero (d.) Infinity 6. The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 104 . The height of the hill is (a.) 250 m (c.) 2.5 km (c.) 1.25 km (d.) 750 m 7. Density of ice is  and that of water is  . What will be the decrease in volume when a mass M of ice melts (a.)  −  M Area = 10–3m2 0.4 m Area=2 × 10–3m2 Q R 10 cm P S 20 cm
(c.) M  −  (c.)       −   1 1 M (d.)       −   1 1 1 M 8. Equal masses of water and a liquid of density 2 are mixed together, then the mixture has a density of (a.) 2/3 (c.) 4/3 (c.) 3/2 (d.) 3 9. A body of density 1 d is counterpoised by Mg of weights of density 2 d in air of density d. Then the true mass of the body is (a.) M (c.)         − 2 1 d d M (c.)         − 1 1 d d M (d.) (1 / ) (1 / ) 1 2 d d M d d − − 10. The pressure at the bottom of a tank containing a liquid does not depend on (a.) Acceleration due to gravity (c.) Height of the liquid column (c.) Area of the bottom surface (d.) Nature of the liquid 11. When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is (a.) H (c.) 2H (c.) 7H (d.) 8H 12. The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is (a.) 5 m (c.) 10 m (c.) 15 m (d.) 20 m 13. The value of g at a place decreases by 2%. The barometric height of mercury (a.) Increases by 2% (c.) Decreases by 2% (c.) Remains unchanged (d.) Sometimes increases and sometimes decreases 14. A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up the reading will be (a.) Zero (c.) Equal to 76 cm (c.) More than 76 cm (d.) Less than 76 cm 15. A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at
(a.) (i) B (ii) D (c.) (i) C (ii) D (c.) (i) B (ii) C (d.) (i) B (ii) A 16. 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.) Increases (c.) Decreases (c.) Remain constant (d.) First decrease and then increase 17. A barometer tube reads 76 cm of mercury. If the tube is gradually inclined at an angle of 60o with vertical, keeping the open end immersed in the mercury reservoir, the length of the mercury column will be (a.) 152 cm (c.) 76 cm (c.) 38 cm (d.) 38 3cm 18. 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 (a.) Half of the radius of the vessel (c.) Radius of the vessel (c.) One-fourth of the radius of the vessel (d.) Three-fourth of the radius of the vessel 19. A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/cm3 ) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/cm3 is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm3 (a.) 10.4 cm (c.) 8.2 cm (c.) 7.2 cm (d.) 9.6 cm 20. A triangular lamina of area A and height h is immersed in a liquid of density  in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is (a.) Agh 2 1 (c.) Agh 3 1 (c.) Agh 6 1 (d.) Agh 3 2 21. If two liquids of same masses but densities 1 and  2 respectively are mixed, then density of mixture is given by (a.) 2 1  2  + = a A D B C Mercury Glycerine 10 cm Oil h
(c.) 1 2 1 2 2     + = (c.) 1 2 2 1 2      + = (d.) 1 2 1 2      + = 22. If two liquids of same volume but different densities 1 and  2 are mixed, then density of mixture is given by (a.) 2 1  2  + = (c.) 1 2 1 2 2     + = (c.) 1 2 2 1 2      + = (d.) 1 2 1 2      + = 23. The density  of water of bulk modulus B at a depth y in the ocean is related to the density at surface  0 by the relation (a.)       = − B gy 0 0 1    (c.)       = + B gy 0 0 1    (c.)       = + hgy Β 0 0 1    (d.)       = − gy B 0 0 1    24. With rise in temperature, density of a given body changes according to one of the following relations (a.) [1 ]  =  0 +  d (c.) [1 ]  =  0 −  d (c.)  =  0 d (d.)  =  0 / d 25. Three liquids of densities d, 2d and 3d are mixed in equal volumes. Then the density of the mixture is (a.) d (c.) 2d (c.) 3d (d.) 5d 26. Three liquids of densities d, 2d and 3d are mixed in equal proportions of weights. The relative density of the mixture is (a.) 7 11d (c.) 11 18 d (c.) 9 13d (d.) 18 23 d 27. From the adjacent figure, the correct observation is Water Water (a) (b)