Fluids Problems

This section provides 100 problems to test your understanding of fluid mechanics, including fluid statics (density, pressure, buoyancy), fluid dynamics (continuity, Bernoulli’s principle), viscosity (Poiseuille’s law, Stokes’ law), and surface tension (capillary action, droplets). Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering fluid mechanics, a key topic for JEE/NEET success.

Numerical Problems

1. A tank filled with water ($\rho =1000{\text{kg/m}}^3$) has a depth of $3\text{m}$. Calculate the pressure at the bottom ($P_{\text{atm}}=1.013\times {10}^5\text{Pa}$, $g=9.8{\text{m/s}}^2$).

   • (a) $1.294\times {10}^5\text{Pa}$
   • (b) $1.307\times {10}^5\text{Pa}$
   • (c) $1.320\times {10}^5\text{Pa}$
   • (d) $1.333\times {10}^5\text{Pa}$

2. A wooden block of density $700{\text{kg/m}}^3$ floats in water ($\rho =1000{\text{kg/m}}^3$). What fraction of the block is submerged?

   • (a) $0.65$
   • (b) $0.70$
   • (c) $0.75$
   • (d) $0.80$

3. A hydraulic lift has an input area $A_1=0.03{\text{m}}^2$ and output area $A_2=0.15{\text{m}}^2$. If an input force $F_1=150\text{N}$ is applied, calculate the output force.

   • (a) $700\text{N}$
   • (b) $725\text{N}$
   • (c) $750\text{N}$
   • (d) $775\text{N}$

4. A steel ball (${\rho }_{\text{steel}}=7800{\text{kg/m}}^3$, volume $0.002{\text{m}}^3$) is submerged in water (${\rho }_{\text{water}}=1000{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). Calculate the buoyant force.

   • (a) $18.6\text{N}$
   • (b) $19.0\text{N}$
   • (c) $19.4\text{N}$
   • (d) $19.6\text{N}$

5. A pipe has cross-sectional areas $A_1=0.04{\text{m}}^2$ and $A_2=0.01{\text{m}}^2$. If the flow speed at $A_1$ is $v_1=1.5\text{m/s}$, calculate $v_2$.

   • (a) $5.5\text{m/s}$
   • (b) $6.0\text{m/s}$
   • (c) $6.5\text{m/s}$
   • (d) $7.0\text{m/s}$

6. A tank with a hole at $2\text{m}$ below the surface releases water. Calculate the speed of the water exiting ($g=9.8{\text{m/s}}^2$).

   • (a) $6.1\text{m/s}$
   • (b) $6.2\text{m/s}$
   • (c) $6.3\text{m/s}$
   • (d) $6.4\text{m/s}$

7. A horizontal pipe has $P_1=1.5\times {10}^5\text{Pa}$, $v_1=2\text{m/s}$, $A_1=0.05{\text{m}}^2$, $A_2=0.02{\text{m}}^2$. Calculate $P_2$ ($\rho =1000{\text{kg/m}}^3$).

   • (a) $1.425\times {10}^5\text{Pa}$
   • (b) $1.430\times {10}^5\text{Pa}$
   • (c) $1.435\times {10}^5\text{Pa}$
   • (d) $1.440\times {10}^5\text{Pa}$

8. An airfoil has $v_{\text{top}}=60\text{m/s}$, $v_{\text{bottom}}=50\text{m/s}$, area $A=1.5{\text{m}}^2$, ${\rho }_{\text{air}}=1.2{\text{kg/m}}^3$. Calculate the lift force.

   • (a) $900\text{N}$
   • (b) $925\text{N}$
   • (c) $950\text{N}$
   • (d) $975\text{N}$

9. A steel ball ($r=0.005\text{m}$, ${\rho }_{\text{steel}}=7800{\text{kg/m}}^3$) falls in oil (${\rho }_{\text{oil}}=800{\text{kg/m}}^3$, $\eta =0.15\text{Pa}\cdot \text{s}$, $g=9.8{\text{m/s}}^2$). Calculate the terminal velocity.

   • (a) $4.70\text{m/s}$
   • (b) $4.80\text{m/s}$
   • (c) $4.90\text{m/s}$
   • (d) $5.00\text{m/s}$

10. A tube of radius $0.004\text{m}$, length $0.2\text{m}$, has $\mathrm{\Delta }P=800\text{Pa}$, $\eta =0.001\text{Pa}\cdot \text{s}$. Calculate the flow rate.

    • (a) $1.61\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (b) $1.63\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (c) $1.65\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (d) $1.67\times {10}^{-5}{\text{m}}^3/\text{s}$

11. A water droplet of radius $0.002\text{m}$ has surface tension $\gamma =0.072\text{N/m}$. Calculate the excess pressure inside.

    • (a) $70\text{Pa}$
    • (b) $72\text{Pa}$
    • (c) $74\text{Pa}$
    • (d) $76\text{Pa}$

12. A capillary tube of radius $0.0004\text{m}$ is placed in water ($\gamma =0.072\text{N/m}$, $\rho =1000{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). Calculate the height of rise.

    • (a) $35.5\text{mm}$
    • (b) $36.0\text{mm}$
    • (c) $36.5\text{mm}$
    • (d) $37.0\text{mm}$

13. A tank filled with mercury ($\rho =13600{\text{kg/m}}^3$) has a depth of $1.5\text{m}$. Calculate the pressure at the bottom ($P_{\text{atm}}=1.013\times {10}^5\text{Pa}$, $g=9.8{\text{m/s}}^2$).

    • (a) $3.00\times {10}^5\text{Pa}$
    • (b) $3.01\times {10}^5\text{Pa}$
    • (c) $3.02\times {10}^5\text{Pa}$
    • (d) $3.03\times {10}^5\text{Pa}$

14. A block of density $400{\text{kg/m}}^3$ floats in a liquid of density $800{\text{kg/m}}^3$. What fraction of the block is submerged?

    • (a) $0.45$
    • (b) $0.50$
    • (c) $0.55$
    • (d) $0.60$

15. A hydraulic lift has $A_1=0.01{\text{m}}^2$ and $A_2=0.05{\text{m}}^2$. If $F_1=100\text{N}$, calculate $F_2$.

    • (a) $450\text{N}$
    • (b) $475\text{N}$
    • (c) $500\text{N}$
    • (d) $525\text{N}$

16. A copper sphere (${\rho }_{\text{copper}}=8900{\text{kg/m}}^3$, volume $0.0005{\text{m}}^3$) is submerged in oil (${\rho }_{\text{oil}}=850{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). Calculate the buoyant force.

    • (a) $4.1\text{N}$
    • (b) $4.2\text{N}$
    • (c) $4.3\text{N}$
    • (d) $4.4\text{N}$

17. A pipe has $A_1=0.06{\text{m}}^2$ and $A_2=0.03{\text{m}}^2$. If $v_1=1\text{m/s}$, calculate $v_2$.

    • (a) $1.5\text{m/s}$
    • (b) $2.0\text{m/s}$
    • (c) $2.5\text{m/s}$
    • (d) $3.0\text{m/s}$

18. A tank with a hole at $1\text{m}$ below the surface releases water. Calculate the exit speed ($g=9.8{\text{m/s}}^2$).

    • (a) $4.3\text{m/s}$
    • (b) $4.4\text{m/s}$
    • (c) $4.5\text{m/s}$
    • (d) $4.6\text{m/s}$

19. A horizontal pipe has $P_1=1.8\times {10}^5\text{Pa}$, $v_1=1.5\text{m/s}$, $A_1=0.03{\text{m}}^2$, $A_2=0.01{\text{m}}^2$. Calculate $P_2$ ($\rho =1000{\text{kg/m}}^3$).

    • (a) $1.775\times {10}^5\text{Pa}$
    • (b) $1.780\times {10}^5\text{Pa}$
    • (c) $1.785\times {10}^5\text{Pa}$
    • (d) $1.790\times {10}^5\text{Pa}$

20. An airfoil has $v_{\text{top}}=70\text{m/s}$, $v_{\text{bottom}}=60\text{m/s}$, $A=2{\text{m}}^2$, ${\rho }_{\text{air}}=1.2{\text{kg/m}}^3$. Calculate the lift force.

    • (a) $1500\text{N}$
    • (b) $1525\text{N}$
    • (c) $1550\text{N}$
    • (d) $1575\text{N}$

21. A glass sphere ($r=0.002\text{m}$, ${\rho }_{\text{glass}}=2500{\text{kg/m}}^3$) falls in water (${\rho }_{\text{water}}=1000{\text{kg/m}}^3$, $\eta =0.001\text{Pa}\cdot \text{s}$, $g=9.8{\text{m/s}}^2$). Calculate the terminal velocity.

    • (a) $0.65\text{m/s}$
    • (b) $0.66\text{m/s}$
    • (c) $0.67\text{m/s}$
    • (d) $0.68\text{m/s}$

22. A tube of radius $0.003\text{m}$, length $0.15\text{m}$, has $\mathrm{\Delta }P=1200\text{Pa}$, $\eta =0.002\text{Pa}\cdot \text{s}$. Calculate the flow rate.

    • (a) $1.27\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (b) $1.28\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (c) $1.29\times {10}^{-5}{\text{m}}^3/\text{s}$
    • (d) $1.30\times {10}^{-5}{\text{m}}^3/\text{s}$

23. A soap bubble of radius $0.015\text{m}$ has surface tension $\gamma =0.025\text{N/m}$. Calculate the excess pressure inside.

    • (a) $6.5\text{Pa}$
    • (b) $6.6\text{Pa}$
    • (c) $6.7\text{Pa}$
    • (d) $6.8\text{Pa}$

24. A capillary tube of radius $0.0002\text{m}$ is placed in water ($\gamma =0.072\text{N/m}$, $\rho =1000{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). Calculate the height of rise.

    • (a) $72.0\text{mm}$
    • (b) $73.0\text{mm}$
    • (c) $74.0\text{mm}$
    • (d) $75.0\text{mm}$

25. A tank filled with oil ($\rho =900{\text{kg/m}}^3$) has a depth of $4\text{m}$. Calculate the pressure at the bottom ($P_{\text{atm}}=1.013\times {10}^5\text{Pa}$, $g=9.8{\text{m/s}}^2$).

    • (a) $1.346\times {10}^5\text{Pa}$
    • (b) $1.347\times {10}^5\text{Pa}$
    • (c) $1.348\times {10}^5\text{Pa}$
    • (d) $1.349\times {10}^5\text{Pa}$

26. A block of density $500{\text{kg/m}}^3$ floats in mercury ($\rho =13600{\text{kg/m}}^3$). What fraction of the block is submerged?

    • (a) $0.035$
    • (b) $0.036$
    • (c) $0.037$
    • (d) $0.038$

27. A hydraulic lift has $A_1=0.02{\text{m}}^2$ and $A_2=0.08{\text{m}}^2$. If $F_1=120\text{N}$, calculate $F_2$.

    • (a) $450\text{N}$
    • (b) $475\text{N}$
    • (c) $480\text{N}$
    • (d) $500\text{N}$

28. A lead sphere (${\rho }_{\text{lead}}=11300{\text{kg/m}}^3$, volume $0.0001{\text{m}}^3$) is submerged in water (${\rho }_{\text{water}}=1000{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). Calculate the buoyant force.

    • (a) $0.95\text{N}$
    • (b) $0.96\text{N}$
    • (c) $0.97\text{N}$
    • (d) $0.98\text{N}$

29. A pipe has $A_1=0.08{\text{m}}^2$ and $A_2=0.04{\text{m}}^2$. If $v_1=0.5\text{m/s}$, calculate $v_2$.

    • (a) $0.8\text{m/s}$
    • (b) $0.9\text{m/s}$
    • (c) $1.0\text{m/s}$
    • (d) $1.1\text{m/s}$

30. A tank with a hole at $0.5\text{m}$ below the surface releases water. Calculate the exit speed ($g=9.8{\text{m/s}}^2$).

    • (a) $3.0\text{m/s}$
    • (b) $3.1\text{m/s}$
    • (c) $3.2\text{m/s}$
    • (d) $3.3\text{m/s}$

31. A horizontal pipe has $P_1=2.0\times {10}^5\text{Pa}$, $v_1=1\text{m/s}$, $A_1=0.06{\text{m}}^2$, $A_2=0.03{\text{m}}^2$. Calculate $P_2$ ($\rho =1000{\text{kg/m}}^3$).

    • (a) $1.995\times {10}^5\text{Pa}$
    • (b) $1.996\times {10}^5\text{Pa}$
    • (c) $1.997\times {10}^5\text{Pa}$
    • (d) $1.998\times {10}^5\text{Pa}$

32. A cylindrical pipe ($r=0.001\text{m}$, $L=0.3\text{m}$, $\eta =0.0015\text{Pa}\cdot \text{s}$) has $Q=5\times {10}^{-6}{\text{m}}^3/\text{s}$. Calculate $\mathrm{\Delta }P$.

    • (a) $1432\text{Pa}$
    • (b) $1433\text{Pa}$
    • (c) $1434\text{Pa}$
    • (d) $1435\text{Pa}$

33. A rocket fuel droplet ($r=0.0002\text{m}$, $\gamma =0.03\text{N/m}$) is atomized. Calculate the excess pressure inside.

    • (a) $300\text{Pa}$
    • (b) $305\text{Pa}$
    • (c) $310\text{Pa}$
    • (d) $315\text{Pa}$

34. A capillary tube of radius $0.0001\text{m}$ is placed in mercury ($\gamma =0.465\text{N/m}$, $\rho =13600{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$, contact angle $\theta ={140}^{\circ }$, $\cos {140}^{\circ }\approx -0.766$). Calculate the depression height.

    • (a) $-50.5\text{mm}$
    • (b) $-51.0\text{mm}$
    • (c) $-51.5\text{mm}$
    • (d) $-52.0\text{mm}$

35. A rocket nozzle (radius $0.04\text{m}$) moves at $150\text{m/s}$ through air ($\eta =1.8\times {10}^{-5}\text{Pa}\cdot \text{s}$). Calculate the viscous drag force.

    • (a) $0.33\text{N}$
    • (b) $0.34\text{N}$
    • (c) $0.35\text{N}$
    • (d) $0.36\text{N}$

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Conceptual Problems

36. What does pressure in a fluid depend on at a given depth?

• (a) Surface area
• (b) Density, gravity, and depth
• (c) Volume of the fluid
• (d) Shape of the container

37. What does Archimedes’ principle state?

• (a) Pressure increases with depth
• (b) Buoyant force equals the weight of displaced fluid
• (c) Fluid speed increases in narrower sections
• (d) Pressure is transmitted equally in a fluid

38. What does the continuity equation imply for an incompressible fluid?

• (a) Pressure is constant
• (b) Flow speed is constant
• (c) Mass flow rate is constant
• (d) Volume decreases with speed

39. What does Bernoulli’s principle conserve in fluid flow?

• (a) Mass
• (b) Momentum
• (c) Energy per unit volume
• (d) Viscosity

40. What is the unit of viscosity?

• (a) $\text{Pa}\cdot \text{s}$
• (b) $\text{N/m}$
• (c) $\text{Pa}$
• (d) $\text{m/s}$

41. What happens to flow speed in a pipe when the cross-sectional area decreases?

• (a) Decreases
• (b) Increases
• (c) Remains the same
• (d) Becomes zero

42. What does a high surface tension indicate?

• (a) Low cohesive forces
• (b) High cohesive forces
• (c) Low viscosity
• (d) High density

43. What is the physical significance of $\frac{2\gamma }{r}$?

• (a) Excess pressure inside a droplet
• (b) Excess pressure inside a soap bubble
• (c) Capillary rise
• (d) Viscous force

44. What does Stokes’ law describe?

• (a) Flow rate in a pipe
• (b) Drag force on a sphere in a fluid
• (c) Pressure in a fluid
• (d) Surface tension in a droplet

45. What is the dimension of surface tension?

• (a) $[\text{M}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

46. What does a zero velocity gradient imply in a fluid?

• (a) No viscous force
• (b) Maximum viscous force
• (c) High flow rate
• (d) Low pressure

47. What is the significance of $\frac{\pi r^4\mathrm{\Delta }P}{8\eta L}$?

• (a) Buoyant force
• (b) Volume flow rate
• (c) Terminal velocity
• (d) Excess pressure

48. What happens to pressure in a fluid as flow speed increases, per Bernoulli’s principle?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

49. What does a low contact angle in capillary action indicate?

• (a) Fluid rises in the tube
• (b) Fluid depresses in the tube
• (c) No rise or depression
• (d) High viscosity

50. How does viscosity affect flow rate in a pipe?

• (a) Increases flow rate
• (b) Decreases flow rate
• (c) No effect
• (d) Increases pressure

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Derivation Problems

51. Derive the pressure in a fluid at depth $P=P_0+\rho gh$.

52. Derive Archimedes’ principle for the buoyant force.

53. Derive the continuity equation $A_1{v}_1=A_2{v}_2$.

54. Derive Bernoulli’s equation for fluid flow.

55. Derive the viscous force equation $F=\eta A\frac{v}{d}$.

56. Derive Poiseuille’s law $Q=\frac{\pi r^4\mathrm{\Delta }P}{8\eta L}$.

57. Derive the excess pressure inside a droplet $\mathrm{\Delta }P=\frac{2\gamma }{r}$.

58. Derive the capillary rise formula $h=\frac{2\gamma \cos \theta }{\rho gr}$.

59. Derive the terminal velocity using Stokes’ law.

60. Derive the velocity of efflux (Torricelli’s law) $v=\sqrt{2gh}$.

61. Derive the lift force on an airfoil using Bernoulli’s principle.

62. Derive the excess pressure inside a soap bubble $\mathrm{\Delta }P=\frac{4\gamma }{r}$.

63. Derive Pascal’s principle for pressure transmission in a hydraulic system.

64. Derive the fraction submerged for a floating object.

65. Derive the viscous drag force on a rocket nozzle using Stokes’ law.

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NEET-style Conceptual Problems

66. What is the unit of pressure in SI units?

• (a) $\text{Pa}$
• (b) $\text{N/m}$
• (c) $\text{J}$
• (d) ${\text{kg/m}}^3$

67. What does a floating object displace in a fluid?

• (a) Fluid equal to its volume
• (b) Fluid equal to its weight
• (c) Fluid equal to its density
• (d) Fluid equal to its surface area

68. Which principle explains the operation of a hydraulic lift?

• (a) Archimedes’ principle
• (b) Bernoulli’s principle
• (c) Pascal’s principle
• (d) Continuity principle

69. What happens to a fluid’s speed in a pipe when the cross-sectional area increases?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

70. What is the dimension of viscosity?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

71. What does Bernoulli’s principle apply to?

• (a) Fluids at rest
• (b) Ideal fluids in steady flow
• (c) Viscous fluids
• (d) Compressible fluids

72. What is the role of surface tension in a droplet?

• (a) Increases volume
• (b) Creates excess pressure inside
• (c) Reduces viscosity
• (d) Increases density

73. What happens to terminal velocity as the radius of a falling sphere increases?

• (a) Decreases
• (b) Increases
• (c) Remains the same
• (d) Becomes zero

74. Why does a fluid rise in a capillary tube with a small radius?

• (a) High viscosity
• (b) Surface tension and low contact angle
• (c) Low density
• (d) High pressure

75. What is the unit of volume flow rate?

• (a) ${\text{m}}^3/\text{s}$
• (b) $\text{m/s}$
• (c) $\text{Pa}$
• (d) $\text{N/m}$

76. What does a constant $Av$ indicate in fluid flow?

• (a) Bernoulli’s principle
• (b) Continuity equation
• (c) Pascal’s principle
• (d) Stokes’ law

77. Which type of force causes lift on an airfoil?

• (a) Viscous force
• (b) Pressure difference
• (c) Buoyant force
• (d) Surface tension

78. What is the direction of the buoyant force?

• (a) Downward
• (b) Upward
• (c) Horizontal
• (d) Along the flow

79. What does a pseudo-force do in a rotating fluid frame?

• (a) Maintains flow rate
• (b) Affects pressure calculations
• (c) Provides buoyant force
• (d) Reduces viscosity

80. What is the dimension of pressure?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

81. What is the role of viscosity in a rocket fuel system?

• (a) Increases flow rate
• (b) Resists flow, affecting fuel delivery
• (c) Increases pressure
• (d) Reduces surface tension

82. What happens to excess pressure inside a droplet as radius decreases?

• (a) Decreases
• (b) Increases
• (c) Remains the same
• (d) Becomes zero

83. Why does Bernoulli’s principle lead to lift on a wing?

• (a) Higher speed, higher pressure
• (b) Higher speed, lower pressure
• (c) Lower speed, lower pressure
• (d) No pressure change

84. What is the significance of $6\pi \eta rv$?

• (a) Buoyant force
• (b) Viscous drag on a sphere
• (c) Surface tension force
• (d) Pressure in a pipe

85. What is the unit of density?

• (a) ${\text{kg/m}}^3$
• (b) $\text{Pa}$
• (c) $\text{N/m}$
• (d) $\text{m/s}$

86. What does a zero flow speed at the surface of a tank indicate?

• (a) No pressure
• (b) Maximum pressure
• (c) Torricelli’s law applies
• (d) No viscosity

87. What is the physical significance of $\sqrt{2gh}$?

• (a) Terminal velocity
• (b) Velocity of efflux
• (c) Capillary rise
• (d) Viscous force

88. Why does a soap bubble have higher excess pressure than a droplet of the same radius?

• (a) Two surfaces vs. one
• (b) Higher surface tension
• (c) Lower viscosity
• (d) Higher density

89. What is the dimension of volume flow rate?

• (a) $[{\text{L}}^3{\text{T}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How does surface tension affect fuel atomization in a rocket?

• (a) Increases droplet size
• (b) Creates pressure to break droplets
• (c) Reduces viscosity
• (d) Increases flow rate

91. What is the role of buoyancy in a hot air balloon?

• (a) Increases pressure
• (b) Provides lift by displacing air
• (c) Increases viscosity
• (d) Reduces surface tension

92. What does a zero pressure difference in a pipe indicate?

• (a) No flow
• (b) Maximum flow
• (c) High viscosity
• (d) Low density

93. What is the physical significance of $\frac{2\gamma \cos \theta }{\rho gr}$?

• (a) Excess pressure
• (b) Terminal velocity
• (c) Capillary rise height
• (d) Flow rate

94. What is the dimension of lift force?

• (a) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does viscosity decrease with temperature in most liquids?

• (a) Increased molecular motion
• (b) Decreased density
• (c) Increased surface tension
• (d) Decreased pressure

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NEET-style Numerical Problems

96. A tank filled with water ($\rho =1000{\text{kg/m}}^3$) has a depth of $1\text{m}$. What is the pressure at the bottom ($P_{\text{atm}}=1.013\times {10}^5\text{Pa}$, $g=9.8{\text{m/s}}^2$)?

• (a) $1.111\times {10}^5\text{Pa}$
• (b) $1.112\times {10}^5\text{Pa}$
• (c) $1.113\times {10}^5\text{Pa}$
• (d) $1.114\times {10}^5\text{Pa}$

97. A pipe has $A_1=0.02{\text{m}}^2$ and $A_2=0.01{\text{m}}^2$. If $v_1=2\text{m/s}$, what is $v_2$?

• (a) $3.5\text{m/s}$
• (b) $4.0\text{m/s}$
• (c) $4.5\text{m/s}$
• (d) $5.0\text{m/s}$

98. A steel ball ($r=0.003\text{m}$, ${\rho }_{\text{steel}}=7800{\text{kg/m}}^3$) falls in water (${\rho }_{\text{water}}=1000{\text{kg/m}}^3$, $\eta =0.001\text{Pa}\cdot \text{s}$, $g=9.8{\text{m/s}}^2$). What is the terminal velocity?

• (a) $2.35\text{m/s}$
• (b) $2.36\text{m/s}$
• (c) $2.37\text{m/s}$
• (d) $2.38\text{m/s}$

99. A water droplet of radius $0.0015\text{m}$ has $\gamma =0.072\text{N/m}$. What is the excess pressure inside?

• (a) $95\text{Pa}$
• (b) $96\text{Pa}$
• (c) $97\text{Pa}$
• (d) $98\text{Pa}$

100. A capillary tube of radius $0.0003\text{m}$ is placed in water ($\gamma =0.072\text{N/m}$, $\rho =1000{\text{kg/m}}^3$, $g=9.8{\text{m/s}}^2$). What is the height of rise?
     - (a) $48.5\text{mm}$
     - (b) $49.0\text{mm}$
     - (c) $49.5\text{mm}$
     - (d) $50.0\text{mm}$

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