JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank

done Critical Thinking Total Questions - 14

• question_answer1)
  A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density 13.6 g/cm3). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water
  A)
                      1.2 cm done clear
  B)
                                                  2.35 cm done clear
  C)
                      0.56 cm done clear
  D)
                      0.8 cm done clear
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• question_answer2)
  A homogeneous solid cylinder of length L\[(L<H/2)\]. Cross-sectional area \[A/5\] is immersed such that it floats with its axis vertical at the liquid-liquid interface with length \[L/4\] in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure \[{{P}_{0}}\]. Then density D of solid is given by                                        [IIT-JEE 1995]
  A)
              \[\frac{5}{4}d\] done clear
  B)
              \[\frac{4}{5}d\] done clear
  C)
              \[d\] done clear
  D)
              \[\frac{d}{5}\] done clear
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• question_answer3)
  A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then [IIT-JEE (Screening) 2002]
  A)
              l decreases and h increases done clear
  B)
              l increases and h decreases done clear
  C)
              Both l and h increase          done clear
  D)
              Both l  and h decrease done clear
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• question_answer4)
  A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm3 is                                                                      [IIT-JEE 1988]
  A)
              3.3  done clear
  B)
              6.4 done clear
  C)
              7.2  done clear
  D)
              12.8 done clear
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• question_answer5)
  A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is   [IIT-JEE 1982]
  A)
              Zero done clear
  B)
              Equal to the weight of the liquid displaced done clear
  C)
              Equal to the weight of the body in air done clear
  D)
              Equal to the weight of the immersed position of the body done clear
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• question_answer6)
  A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is \[\omega \], then the difference in the heights of the liquid at the centre of the vessel and the edge is
  A)
              \[\frac{r\omega }{2g}\]     done clear
  B)
              \[\frac{{{r}^{2}}{{\omega }^{2}}}{2g}\] done clear
  C)
              \[\sqrt{2gr\omega }\]        done clear
  D)
               \[\frac{{{\omega }^{2}}}{2g{{r}^{2}}}\] done clear
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• question_answer7)
  Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2) [IIT JEE 2004]
  A)
   50 m2/s2                                              done clear
  B)
   50.5 m2/s2                                          done clear
  C)
   51 m2/s2                                              done clear
  D)
   52 m2/s2 done clear
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• question_answer8)
  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 the holes are the same. Then R is equal to                         [IIT-JEE (Screening) 2000]
  A)
              \[2\pi \,L\]                              done clear
  B)
              \[\frac{L}{\sqrt{2\pi }}\] done clear
  C)
              L      done clear
  D)
              \[\frac{L}{2\pi }\] done clear
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• question_answer9)
  A cylinder containing water up to a height of 25 cm has a hole of cross-section \[\frac{1}{4}c{{m}^{2}}\] in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
  A)
              Increase of 12.5 gm-wt     done clear
  B)
              Increase of 6.25 gm-wt     done clear
  C)
              Decrease of 12.5 gm-wt done clear
  D)
              Decrease of 6.25 gm-wt done clear
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• question_answer10)
  There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density \[\rho \]. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is 
  A)
              \[gh\rho a\] done clear
  B)
              \[\frac{2gh}{\rho \,a}\] done clear
  C)
              \[2\rho agh\] done clear
  D)
              \[\frac{\rho gh}{a}\] done clear
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• question_answer11)
  Two communicating vessels contain mercury. The diameter of one vessel is n times larger 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 \[\rho \] = density of water) by
  A)
              \[\frac{{{n}^{2}}h}{{{(n+1)}^{2}}s}\]                                        done clear
  B)
              \[\frac{h}{({{n}^{2}}+1)\,s}\] done clear
  C)
              \[\frac{h}{{{(n+1)}^{2}}s}\]      done clear
  D)
              \[\frac{h}{{{n}^{2}}s}\] done clear
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• question_answer12)
  A uniform rod of density \[\rho \] is placed in a wide tank containing a liquid of density \[{{\rho }_{0}}({{\rho }_{0}}>\rho )\]. The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod makes an angle \[\theta \] with the horizontal
  A)
              \[\sin \theta =\frac{1}{2}\sqrt{{{\rho }_{0}}/\rho }\]        done clear
  B)
              \[\sin \theta =\frac{1}{2}\,.\,\frac{{{\rho }_{0}}}{\rho }\] done clear
  C)
              \[\sin \theta =\sqrt{\rho /{{\rho }_{0}}}\]                             done clear
  D)
              \[\sin \theta ={{\rho }_{0}}/\rho \] done clear
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• question_answer13)
  A block of ice floats on a liquid of density 1.2in a beaker then level of liquid when ice completely melt  [IIT-JEE 1994]
  A)
              Remains same                       done clear
  B)
              Rises done clear
  C)
              Lowers                                     done clear
  D)
              (a), (b) or (c) done clear
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• question_answer14)
  A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from \[{{H}_{1}}\] to \[{{H}_{2}}\] will be
  A)
              \[\frac{A}{a}\sqrt{\frac{2}{g}}[\sqrt{{{H}_{1}}}-\sqrt{{{H}_{2}}}]\]                                 done clear
  B)
              \[\sqrt{2gh}\] done clear
  C)
              \[\sqrt{2gh\,({{H}_{1}}-{{H}_{2}})}\]                                        done clear
  D)
               \[\frac{A}{a}\sqrt{\frac{g}{2}}[\sqrt{{{H}_{1}}}-\sqrt{{{H}_{2}}}]\] done clear
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