NEET Mechanical Properties of Fluids — Set 22

Question 1

A manometer with mercury ($ \rho = 13.6 \times 10^3 \, \text{kg/m}^3 $) shows a height difference of $ 20 \, \text{cm} $. What is the pressure difference? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ \Delta P = \rho g h $. $ \rho = 13.6 \times 10^3 \, \text{kg/m}^3 $, $ g = 9.8 \, \text{m/s}^2 $, $ h = 0.2 \, \text{m} $. $ \Delta P = 13.6 \times 10^3 \times 9.8 \times 0.2 = 26656 \, \text{Pa} $.

Question 2

A soap bubble of radius $ 6 \, \text{mm} $ has a surface tension of $ 0.03 \, \text{N/m} $. What is the excess pressure inside?

Accepted Answer

Excess pressure in a bubble: $ \Delta P = \frac{4 S}{r} $. $ S = 0.03 \, \text{N/m} $, $ r = 6 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{4 \times 0.03}{6 \times 10^{-3}} = 20 \, \text{Pa} $.

Question 3

A manometer with whole blood ($ \rho = 1.06 \times 10^3 \, \text{kg/m}^3 $) shows a height difference of $ 0.18 \, \text{m} $. What is the pressure difference? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ \Delta P = \rho g h $. $ \rho = 1.06 \times 10^3 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $, $ h = 0.18 \, \text{m} $. $ \Delta P = 1.06 \times 10^3 \times 10 \times 0.18 = 1908 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 22

Q1. A manometer with mercury (\( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \)) shows a height difference of \( 20 \, \text{cm} \). What is the pressure difference? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q2. A soap bubble of radius \( 6 \, \text{mm} \) has a surface tension of \( 0.03 \, \text{N/m} \). What is the excess pressure inside?

Q3. A manometer with whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \)) shows a height difference of \( 0.18 \, \text{m} \). What is the pressure difference? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. What is the force on a submarine window (\( 0.08 \, \text{m}^2 \)) at \( 300 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)), interior at atmospheric pressure? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. What is the physical significance of the term \( \frac{1}{2} \rho v^2 \) in Bernoulli’s equation?

Q6. A spray tube (\( 7 \, \text{cm}^2 \)) has 35 holes of diameter \( 1.2 \, \text{mm} \). If the flow speed is \( 3.0 \, \text{m/min} \), what is the ejection speed?

Q7. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 3.5 \, \text{m/s} \) with pressure \( 1.7 \times 10^5 \, \text{Pa} \). If the speed rises to \( 6 \, \text{m/s} \), what is the new pressure?

Q8. Water flows at \( 2.9 \, \text{m/s} \) at \( 3.2 \, \text{m} \) height with pressure \( 1.9 \times 10^5 \, \text{Pa} \). What is the pressure at \( 1.8 \, \text{m} \) height with speed \( 4.0 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Q9. A plate of area \( 0.07 \, \text{m}^2 \) moves at \( 0.3 \, \text{m/s} \) over a \( 0.5 \, \text{mm} \) thick water film (\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \)). What force is required?

Q10. Why does a hydraulic lift amplify force when lifting a heavy load?