Title 4.FLUID MECHANICS_Final (37-58).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 3 7 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., FLUID MECHANICS FLUID MECHANICS LEVEL-V SINGLE ANSWER TYPE QUESTIONS 1. A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and mass M. It is suspended by a string in a liquid of density  , where it stays vertical. the upper surface of cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is a)   2   g V R h  b) Mg c) Mg V g   d) 2 Mg R h g   2. A closed compartment containing liquid (as shown) is moving with an acceleration along x - axis. Find the incorrect statement a) The pressure at A and O is same b) The pressure at O and O1 is same c) The pressure at B and C is same d) The pressure at D and E is same 3. A cylinder stands vertical in two immiscible liquids of densities  and 2 liquids are shown. Find the difference in pressure at point A and B: a) 2gh b) 3gh c) 4gh d) None 4. A vessel of height H and length L contains a liquid of density  upto height H/2. The vessel starts accelerating horizontally with acceleration ‘ a ’ towards right. If A is the point at the surface of the liquid at right end while the vessel is accelerating and B is the point at bottom of the vessel on the other end, the difference of pressure at B and A will be. a)   2 gH aL   b)   2 gH aL   c) 2  gH aL   d)   3 2 gH aL   5. In the syphon as shown, which of the option is not correct, if 2 1 h h  and 3 1 h h  ? a) E D p p  b) E C p p  c) B C p p  d) B E p p 
3 8 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., FLUID MECHANICS 6. Equal volumes of two immiscible liquids of densities  and 2 are filled in a vessel as shown in figure. Two small holes are punched at depth 2 h and 3 2 h from the surface of lighter liquid. If 1 v and 2 v are the velocities of efflux at these two holes, then 1 2 v v is : a) 1 2 2 b) 1 2 c) 1 4 d) 1 2 7. The velocity of the liquid coming out of a small hole of a vessel containing two different liquids of densities 2 and  as shown in Fig is   2h h a) gh b) 2 gh c) 2 2gh d) 6gh 8. The Fig. shows a semi-cylindrical massless gate of unit length perpendicular to the plane of the page and is pivoted at the point O holding a stationary liquid of density  . A horizontal force F is applied at its lowest position to keep it stationary. The magnitude of the force is : a) 3 2 2  gR b) 9 2 2  gR c) 2 gR d) none 9. A light semi-cylindrical gate of radius R is pivoted at its mid point O, of the diameter as shown in the figure holding liquid of density  . The force F required to prevent the rotation of the gate is equal to: a) 3 2  R g b) 3 2gR l c) 2 2 3 R l g  d) None 10. 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) 1/3 7 2 b) 1/3 5 2 c) 1/3 9 2 d) 1/3 3 2 11. A cylindrical tank of height H is open at the top end and it has a radius R. water is filled in it up to a height of h. The time taken to empty the tank through a hole of radius r in its bottom is a) 2 2 2h R g r b) 2 2 2H R g r . c) hH d) 2H R g r 12. Two unequal blocks placed over each other of different densities 1 and  2 are immersed in fluid of density  . The block of density 1 is fully submerged and the block of density  2 is partly submerged so that raito of their masses is 1/2 and 1  / 2  and 2  / 0.5  . Find the degree of submergence of the upper block of density  2 . a) 50% submerged b) 25% submerged c) 75% submerged d) Fully submerged
NISHITH Multimedia India (Pvt.) Ltd., 3 9 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., FLUID MECHANICS MORE THAN ONE CORRECT 13. In the siphon system shown below, v refers to velocity and P refers to pressure. Then: a) E A v v  b)   P P g h h D    0 1 2  c) A B E v v v   d) 5 E A B v v v   14. Three different liquids are filled in a U-tube as shown in Fig. Their densities are 1 2  , and 3 respectively. From the Fig. we may conclude that: a)   2 1  b)   1 2  c)    3 2 1   2 2   d) 2 1 3 2      15. There are two holes on a water tank as shown in Fig. Area of hole 2 is two times that of area of hole 1. Suppose v is the speed of liquid coming out and Q the volume of liquid flowing per second. Then: a) 1 2 v v  4 b) 1 2 v v  2 c) Q Q 1 2  d) 1 2 Q Q  2 16. The area of two holes A and B are 2 a and a respectively. The holes are at height (H/3) and (2H/3) from surface of water a) The velocity of efflux at hole B is 2 times the velocity of efflux at hole A b) The velocity of efflux at hole B is 2 times the velocity of efflux at hole A c) The discharge is same through both the holes d) The discharge through hole A is 2 time the discharge through hole B. 17. The figure shows a container filled with a liquid of density  . Four points A, B, C and D lie 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) P P D B  b) P P P P A B D C    c) 2 C A D B P P P P    d) 2 C A D B P P P P    COMPREHENSION TYPE QUESTIONS Comprehension : I Block A in the Fig. hangs from a spring balance D and is submerged in a liquid C contained in beaker B. The weight of beaker is 1kg, and the weight of the liquid is 1.5kg. The balance D reads 2.5kg and balance E reads 7.5kg. The volume of the block is 0.003 3 m .
4 0 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - IV NISHITH Multimedia India (Pvt.) Ltd., FLUID MECHANICS 18. What is the density of the liquid? a) 3 1666.7 / kg m b) 3 1500 / kg m c) 3 2500 / kg m d) 3 1750 / kg m 19. When A is taken out, what will be the reading of D? a) 7.5Kg b) 2kg c) 3.5kg d) 2.1kg 20. When A is taken out, what will be the reading of E? a) 2.5 kg b) 2kg c) 1.5 kg d) 3 kg Comprehension : II An open rectangular tank of dimensions 6m x 5m x 4m contains water upto a height of 2m. The vessel is accelerated horizontally with an acceleration of a 2 m s/ as shown. Take 3 3 water   10 / kg m , 2 g m s 10 / , atmospheric pressure = 5 2 10 / N m . Base on above information answer the following questions: 21. Determine the maximum value of a so that no water comes out from tank. a) g b) 2 3 g c) 3 g d) 2g 22. Determine the height to which the water should be filled in the tank so that when 2 a m s  5 / , no water comes out from the tank. a) 2m b) 3m c) 2.5m d) 3.5m 23. If instead of open top, the vessel is closed, then absolute pressure at point A would be: [ Take 20 2 / 3 a m s  and initially height of water in tank is 2m] a) 5 2 1.33 10 /  N m b) 5 2 1.0 10 /  N m c) 45 2 3.33 10 /  N m d) None Comprehension : III . A solid hemisphere of radius R is made to just sink in a liquid of density  . Find the 24. vertical thrust on the curved surface a) 3 3   R g b) 3 2   R g c) 0 d) 3   R g 25. Vertical thrust on the flat surface a) 3 3   R g b) 3 2   R g c) 0 d) 3   R g 26. Side thrust on the hemisphere a) 3 3   R g b) 3 2   R g c) 0 d) 3   R g Comprehension : IV A tortoise is just sinking in water of density  . The tortoise is assumed to be a hemisphere of radius R. 27. Find the horizontal thrust a) 3  g R b) 1 3 3  g R c) 2 3 3  g R d) 0 28. Find Vertical thrust a) 3  g R b) 1 3 3  g R c) 2 3 3  g R d) 0