NEET Mechanical Properties of Fluids — Set 8

Question 1

A bubble of radius $ 6.5 \, \text{mm} $ is blown at $ 55 \, \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 = 9.8 \, \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 9.8 \times 0.55 = 5390 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.0727}{6.5 \times 10^{-3}} = 22.34 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 5390 + 22.34 = 1.06392 \times 10^5 \, \text{Pa} $.

Question 2

A hydraulic lift uses a small piston of area $ 0.02 \, \text{m}^2 $ to exert a force of $ 200 \, \text{N} $ to lift a load with a large piston of area $ 0.1 \, \text{m}^2 $. What is the mass of the load? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Pascal’s law: $ P = \frac{F_1}{A_1} = \frac{F_2}{A_2} $. $ F_2 = F_1 \times \frac{A_2}{A_1} $. $ F_1 = 200 \, \text{N} $, $ A_1 = 0.02 \, \text{m}^2 $, $ A_2 = 0.1 \, \text{m}^2 $. $ F_2 = 200 \times \frac{0.1}{0.02} = 200 \times 5 = 1000 \, \text{N} $. $ m = \frac{F_2}{g} = \frac{1000}{10} = 100 \, \text{kg} $.

Question 3

A $ 65 \, \text{kg} $ person stands on two bones, each with area $ 20 \, \text{cm}^2 $. What is the average pressure on the bones? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ P_{av} = \frac{F}{A} $, $ F = mg = 65 \times 10 = 650 \, \text{N} $. Total area $ A = 2 \times 20 \times 10^{-4} = 4.0 \times 10^{-3} \, \text{m}^2 $. $ P_{av} = \frac{650}{4.0 \times 10^{-3}} = 1.625 \times 10^5 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 8

Q1. A bubble of radius \( 6.5 \, \text{mm} \) is blown at \( 55 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 9.8 \, \text{m/s}^2 \))

Q2. A hydraulic lift uses a small piston of area \( 0.02 \, \text{m}^2 \) to exert a force of \( 200 \, \text{N} \) to lift a load with a large piston of area \( 0.1 \, \text{m}^2 \). What is the mass of the load? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 65 \, \text{kg} \) person stands on two bones, each with area \( 20 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A spray tube (\( 6 \, \text{cm}^2 \)) has 30 holes of diameter \( 1.2 \, \text{mm} \). If the flow speed is \( 1.8 \, \text{m/min} \), what is the ejection speed?

Q5. A plate of area \( 0.09 \, \text{m}^2 \) moves at \( 0.5 \, \text{m/s} \) over a \( 1.0 \, \text{mm} \) thick water film (\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \)). What force is required?

Q6. A spray tube (\( 5 \, \text{cm}^2 \)) has 25 holes of diameter \( 1.0 \, \text{mm} \). If the flow speed is \( 2.4 \, \text{m/min} \), what is the ejection speed?

Q7. A pipe’s cross-sectional area decreases from \( 0.09 \, \text{m}^2 \) to \( 0.03 \, \text{m}^2 \). If water flows at \( 1.5 \, \text{m/s} \) in the larger section, what is the speed in the smaller section?

Q8. A capillary tube of radius \( 0.4 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q9. Water flows at \( 1.8 \, \text{m/s} \) at \( 2.8 \, \text{m} \) height with pressure \( 1.75 \times 10^5 \, \text{Pa} \). What is the pressure at \( 1.2 \, \text{m} \) height with speed \( 2.6 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Q10. A soap film supports \( 3.0 \times 10^{-2} \, \text{N} \) over a \( 50 \, \text{cm} \) slider. What is the surface tension?

Q11. What causes the pressure inside a soap bubble to be higher than outside?

Q12. A capillary tube of radius \( 0.15 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q13. A car lift uses a small piston of radius \( 4 \, \text{cm} \) to lift a \( 1200 \, \text{kg} \) car on a piston of radius \( 12 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. A plate of area \( 0.06 \, \text{m}^2 \) moves at \( 0.9 \, \text{m/s} \) over a \( 0.5 \, \text{mm} \) thick honey film (\( \eta = 0.2 \, \text{Pa s} \)). What force is required?

Q15. What is the gauge pressure at a depth of \( 2.9 \, \text{m} \) in water (\( \rho = 1000 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))