MECHANICAL PROPERTIES OF FLUIDS(10-01-2021)

1. A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the

Curve A

Curve B

Curve C

Curve D

2. Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has radius equal to

$\frac{r_{1}+r_{2}}{2}$

$\frac{r_{1}r_{2}}{r_{1}+r_{2}}$

$\sqrt{r_{1}r_{2}}$

$\sqrt{r_{1}^{2}+r_{2}^{2}}$

3. Water stands at level A in the arrangement shown in the figure. What will happen if a jet of air is gently blown into the horizontal tube in the direction shown in the figure?

Water will rise above A in the capillary tube

Water will fall below A in the capillary tube

There will be no effect on the level of water in the capillary tube

Air will emerge from end B in the form of bubbles

4. Water is flowing through a horizontal pipe of varying cross-section. If the pressure of water equals 2 cm of mercury, where the velocity of the flow is 32 $cm\, s^{-1}$ , what is the pressure at another point, where the velocity of flow is $65cm\, s^{-1}$ ?

1.02 cm of Hg

1.88 cm of Hg

2.42 cm of Hg

1.45 cm of Hg

5. From the adjacent figure, the correct observation is

the pressure on the bottom of the tank A is greater than at the bottom of B

the pressure on the bottom of the tank A smaller than at the bottom of B

the pressure depends on the shape of the container

the pressure on the bottom of A and B is the same

6. When a glass capillary tube of radius 0.015 cm is dipped in water, the water rises to height of 15 cm within it. Assuming contact angle between water and glass to be $0^{0}$ , the surface tension of water is $\left [ \rho _{water}=1000kg\, m^{-3},g=9.81ms^{-2} \right ]$

$0.11Nm^{-1}$

$0.7Nm^{-1}$

$0.072Nm^{-1}$

None of these

7. An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

3.0 m/s

1.5 m/s

1.0 m/s

2.25 m/s

8. A mercury drop of radius 1.0 cm is sprayed in to $10^{6}$ droplets of equal size. The energy expended in this process is (surface tension of mercury is equal to $32\times 10^{-2}Nm^{-1}$ )

$3.98\times 10^{-4}J$

$8.46\times 10^{-4}J$

$3.98\times 10^{-2}J$

$3.98\times 10^{-3}J$

9. If there were no gravity, which of the following will not be there for fluid?

Viscosity

Surface tension

Pressure

Archimedes’ upward thrust

10. The surface area of air bubble increases four times when it rises from bottom to top of a water tank where the temperature is uniform. If the atmospheric pressure is 10 m of water, the depth of the water in the tank is

30 m

40 m

70 m

80 m

11. For a liquid which is rising in a capillary, the angle of contact is

Obtuse

180°

Acute

90°

12. Water in a vessel of uniform cross-section escapes through a narrow tube at the base of the vessel. Which graph given below represents the variation of the height h of the liquid with time ?

13. A cylinder is filled with liquid of density d upto a height h. If the cylinder is at rest, then the mean pressure of the walls is

hdg/4

hdg/2

2 hdg

hdg

14. If the rise in height of capillary of two tubes are 6.6 cm and 2.2 cm, then the ratio of the radii of tubes is

1:3

3:1

1:2

1:6

15. The excess pressure inside a spherical drop of water is four time that of another drop. Then their respective mass ratio is

1:16

8:1

1:4

1:64

16. A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides (figure). If the radius of the vessel is 0.05 m and the sped of rotation is $2rad\, s^{-1}$ , find the difference in the height of the liquid at the centre of the vessel and its sides

20 cm

4 cm

2 cm

0.2 cm

17. Surface tension of a soap solution is able of 2.0 cm diameter will be

$7.6\times 10^{-6}\pi J$

$15.2\times 10^{-6}\pi J$

$1.9\times 10^{-6}\pi J$

$1\times 10^{-4}\pi J$

18. The viscous force acting on a rain drop of radius 0.35 mm falling through air with a velocity of $1ms^{-1}$ , is $\left ( \eta =2\times 10^{-4}Nsm^{-2} \right )$

$6.6\times 10^{-6}N$

$6.6\times 10^{-5}N$

$1.32\times 10^{-7}N$

$13.2\times 10^{-7}N$

19. An air-tight cage with a parrot sitting in it is suspended from the spring balance. The parrot starts flying. The reading of the spring balance will

Increase

Decrease

Not change

Be zero

20. A rain drop of radius 1.5 mm, experiences a drag force $F=\left ( 2\times 10^{-5}v \right )$ N, while falling through air from a height 2 km, with a velocity v. The terminal velocity of the rain drop will be nearly (use $g=10ms^{-2}$ )

$200ms^{-1}$

$80ms^{-1}$

$7ms^{-1}$

$3ms^{-1}$

21. A liquid flows through a pipe of non-uniform cross-section. If $A_{1}$ and $A_{2}$ are the cross-sectional area of the pipe at two points, the ratio of velocities of the liquid at these points will be

$A_{1}A_{2}$

$\frac{A_{1}}{A_{2}}$

$\frac{A_{2}}{A_{1}}$

$\frac{1}{A_{1}A_{2}}$

22. A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body

It will slowly come back to its earlier position

It will remain submerged, where it is left

It will sink

It will come out violently

23. A balloon of volume 1500 $m^{3}$ and weighing 1650 kg with all its equipment is filled with He (density $0.2 kg \,m^{-3}$ ). If the density of air be $1.3kgm^{-3}$ , the pull on the rope tied to the balloon will be

300 kg

1950 kg

1650 kg

Zero

24. There are two holes one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is 0.01 $m^{2}$ and the vertical distance between the holes is one meter. The tank is filled with water flows out of the holes is (density of water $=1000kgm^{-3})$

100

200

300

400

25. The terminal velocity of spherical ball of radius a falling through a viscous liquid is proportional to

$a^{2}$

$a^{3}$

$a^{-1}$

26. In making an alloy, a substance of specific gravity $s_{1}$ and mass $m_{1}$ is mixed with another substance of specific gravity $s_{2}$ and mass $m_{2}$ : then the specific gravity of the alloy is

$\left ( \frac{m_{1}+m_{2}}{s_{1}+s_{2}} \right )$

$\left ( \frac{s_{1}s_{2}}{m_{1}+m_{2}} \right )$

$\frac{m_{1}+m_{2}}{\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}}$

$\frac{\frac{m_{1}}{s_{1}}+\frac{m_{2}}{s_{2}}}{m_{1}+m_{2}}$

27. A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film. When the portion A is punctured with a pin, the thread

Becomes concave towards A

Becomes convex towards A

Either (a) or (b) depending on the size of A with respect to B

Remain in the initial position

28. The pressure on a swimmer 20 m below the surface of water at sea level is

1.0 atm

2.0 atm

2.5 atm

3.0 atm

29. A barometer tube reds 76m of mercury. If the tube is gradually inclined at an angle of $60^{0}$ with vertical, keeping the open end immersed in the mercury reservoir, the length of the mercury column will be

152 cm

76 cm

38 cm

$38\sqrt{3}cm$

30. Water from a tap emerges vertically downwards with an initial speed of $1.0ms^{-1}$ . The cross-sectional area of the tap is $10^{-4}m^{2}$ . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is

$1.0\times 10^{-5}m^{2}$

$2\times 10^{-5}m^{2}$

$5\times 10^{-5}m^{2}$

$5\times 10^{-4}m^{2}$

31. A square wire frame of size L is dipped in a liquid. On taking out a membrane is formed. If the surface tension of liquid is T, then the force acting on a frame will be

2 T/L

4T/L

8 T/L

16 T/L

32. A glass flask having mass 390 g and an interior volume of $500cm^{3}$ floats on water when it is less than half filled with water. The density of the material of the flask is

$0.8g\,cc^{-1}$

$2.8g\,cc^{-1}$

$1.8g\,cc^{-1}$

$0.28g\,cc^{-1}$

33. If two soap bubbles of different radii are connected by a tube

air flows from the bigger bubble to the smaller bubble till the sizes become equal

air flows from bigger bubble to the smaller bubble till the sizes are interchanged

air flows from the smaller bubble to the bigger

there is no flow of air

34. A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D>d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is

$\sqrt{\frac{2h}{g}}$

$\sqrt{\frac{2h}{g}.\frac{D}{d}}$

$\sqrt{\frac{2h}{g}.\frac{d}{D}}$

$\sqrt{\frac{2h}{g}}\left ( \frac{d}{D-d} \right )$

35. Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is p at a point where flow speed is v, the pressure at another point where the flow of speed is 2v, is (take density of water as $\rho$ )

$p-\frac{3\rho v^{2}}{2}$

$p-\frac{\rho v^{2}}{2}$

$p-\frac{3\rho v^{2}}{4}$

$p-\rho v^{2}$

36. On which of the following, the terminal velocity of a solid ball in a viscous fluid is independent?

Area of cross-section

Height of the liquid

Density of the ball

Density of the liquid

37. A container with square base of side a hight H with a liquid. A hole is made at a depth h from the free surface of water. With what acceleration the container must be accelerated, so that the water does not come out?

$\frac{g}{2}$

$\frac{2gH}{2}$

$\frac{2gh}{a}$

38. Two drops of the same radius are falling through air with a steady velocity of 5cm per sec. If the two drops coalesce, the terminal velocity would be

10 cm per sec

2.5 cm per sec

$5\times \left ( 4 \right )^{1/3}cm\, per\, sec$

$5\times \sqrt{2}cm\, per\, sec$

39. A liquid flows in a tube from left to right as shown in figure $A_{1}$ and $A_{2}$ are the cross-sections of the portions of the tube as shown. Then the ratio of speeds $v_{1}/v_{2}$ will be

$A_{1}/A_{2}$

$A_{2}/A_{1}$

$\sqrt{A_{2}}/\sqrt{A_{1}}$

$\sqrt{A_{1}}/\sqrt{A_{2}}$

40. A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes $T_{1}$ time to decrease the height of water to $\frac{H}{\eta }\left ( \eta >1 \right ):$ and it takes $T_{2}$ time to take out the rest of water. If $T_{1}=T_{2}$ , then the value of $\eta$ is

$2\sqrt{2}$

41. The meniscus of mercury in a capillary glass tube, is

Concave

Plane

Cylindrical

convex

42. Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $\rho$ , the surface tension of water is T and the atmospheric pressure is $P_{0}$ . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

$\left | 2P_{0}Rh+\pi R^{2}\rho gh-2RT \right |$

$\left | 2P_{0}Rh+R\rho gh^{2}-2RT \right |$

$\left | P_{0}\pi R^{2}+R\rho gh^{2}-2RT \right |$

$\left | P_{0}\pi R^{2}+R\rho gh^{2}+2RT \right |$

43. What is the radius of the biggest aluminium coin of thickness t and density $\rho$ , which will still be able to float on the water surface of surface tension ?

$\frac{4S}{3\rho \,g\,t}$

$\frac{3S}{4\rho \,g\,t}$

$\frac{2S}{\rho \,g\,t}$

$\frac{S}{\rho \,g\,t}$

44. In the figure, the velocity $V_{3}$ will be

Zero

$4ms^{-1}$

$1ms^{-1}$

$3ms^{-1}$

45. A uniform long tube is bent into a circle of radius R and it lies in a vertical plane. Two liquids of same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is