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