NEET Mechanical Properties of Fluids — Set 4

Question 1

A sphere of radius $ 0.05 \, \text{m} $ moves at $ 0.11 \, \text{m/s} $ through blood ($ \eta = 2.7 \times 10^{-3} \, \text{Pa s} $). What is the viscous drag force?

Accepted Answer

Stokes’ law: $ F = 6 \pi \eta a v $. $ \eta = 2.7 \times 10^{-3} \, \text{Pa s} $, $ a = 0.05 \, \text{m} $, $ v = 0.11 \, \text{m/s} $. $ F = 6 \times 3.14 \times 2.7 \times 10^{-3} \times 0.05 \times 0.11 = 0.0028 \, \text{N} $.

Question 2

What is the excess pressure inside a water drop of radius $ 2.5 \, \text{mm} $ at $ 20^\circ \text{C} $? (Surface tension = $ 0.0727 \, \text{N/m} $)

Accepted Answer

Excess pressure: $ \Delta P = \frac{2 S}{r} $. $ S = 0.0727 \, \text{N/m} $, $ r = 2.5 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{2 \times 0.0727}{2.5 \times 10^{-3}} = 58.16 \, \text{Pa} $.

Question 3

A bubble of radius $ 5.5 \, \text{mm} $ is blown at $ 45 \, \text{cm} $ depth in water ($ \rho = 1000 \, \text{kg/m}^3 $, $ S = 0.0727 \, \text{N/m} $). What is the total pressure inside? (Take $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ P_i = P_a + \rho g h + \frac{2 S}{r} $. $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ \rho g h = 1000 \times 10 \times 0.45 = 4500 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.0727}{5.5 \times 10^{-3}} = 26.44 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 4500 + 26.44 = 1.05526 \times 10^5 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 4

Q1. A sphere of radius \( 0.05 \, \text{m} \) moves at \( 0.11 \, \text{m/s} \) through blood (\( \eta = 2.7 \times 10^{-3} \, \text{Pa s} \)). What is the viscous drag force?

Q2. What is the excess pressure inside a water drop of radius \( 2.5 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.0727 \, \text{N/m} \))

Q3. A bubble of radius \( 5.5 \, \text{mm} \) is blown at \( 45 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 10 \, \text{m/s}^2 \))

Q4. What is the absolute pressure at \( 450 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) with \( P_a = 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. Which statement is incorrect about Stokes’ law?

Q6. A soap film supports \( 2.2 \times 10^{-2} \, \text{N} \) over a \( 44 \, \text{cm} \) slider. What is the surface tension?

Q7. What is the reason a small insect can walk on water?

Q8. Why does the pressure inside a liquid drop exceed the external pressure?

Q9. Why does a fluid at rest exert the same pressure at all points at the same horizontal level?

Q10. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 4.2 \, \text{m/s} \) with pressure \( 1.95 \times 10^5 \, \text{Pa} \). If the speed increases to \( 6.5 \, \text{m/s} \), what is the new pressure?

Q11. A tank has a hole \( 1.4 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q12. A soap film supports \( 1.8 \times 10^{-2} \, \text{N} \) over a \( 35 \, \text{cm} \) slider. What is the surface tension?

Q13. A hydraulic lift raises a \( 1700 \, \text{kg} \) load using a small piston of radius \( 3.5 \, \text{cm} \) and a large piston of radius \( 14 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. What is the total pressure at a depth of \( 2.2 \, \text{m} \) in hydrogen liquid (\( \rho = 9.0 \times 10^{-2} \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q15. A manometer with water (\( \rho = 1000 \, \text{kg/m}^3 \)) shows a height difference of \( 0.15 \, \text{m} \). What is the pressure difference? (Take \( g = 9.8 \, \text{m/s}^2 \))