NEET Mechanical Properties of Fluids — Set 14

Question 1

A bubble of radius $ 2.5 \, \text{mm} $ is blown at $ 20 \, \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 0.2 = 1960 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.0727}{2.5 \times 10^{-3}} = 58.16 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 1960 + 58.16 = 1.02958 \times 10^5 \, \text{Pa} $.

Question 2

A tank has a hole $ 1.5 \, \text{m} $ below the water surface, open to the atmosphere. What is the efflux speed? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Torricelli’s law: $ v = \sqrt{2 g h} $. $ g = 10 \, \text{m/s}^2 $, $ h = 1.5 \, \text{m} $. $ v = \sqrt{2 \times 10 \times 1.5} = \sqrt{30} \approx 5.48 \, \text{m/s} $.

Question 3

What is the excess pressure inside a mercury drop of radius $ 1.5 \, \text{mm} $ at $ 20^\circ \text{C} $? (Surface tension = $ 0.4355 \, \text{N/m} $)

Accepted Answer

Excess pressure: $ \Delta P = \frac{2 S}{r} $. $ S = 0.4355 \, \text{N/m} $, $ r = 1.5 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{2 \times 0.4355}{1.5 \times 10^{-3}} = 580.67 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 14

Q1. A bubble of radius \( 2.5 \, \text{mm} \) is blown at \( 20 \, \text{cm} \) 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 tank has a hole \( 1.5 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. What is the excess pressure inside a mercury drop of radius \( 1.5 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.4355 \, \text{N/m} \))

Q4. Water flows at \( 2.3 \, \text{m/s} \) at \( 3.5 \, \text{m} \) height with pressure \( 1.6 \times 10^5 \, \text{Pa} \). What is the pressure at \( 1.5 \, \text{m} \) height with speed \( 3.2 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \))

Q5. What is the total pressure at a depth of \( 4 \, \text{m} \) in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) if atmospheric pressure is \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 5.0 \, \text{m/s} \) with pressure \( 2.1 \times 10^5 \, \text{Pa} \). If the speed increases to \( 7.5 \, \text{m/s} \), what is the new pressure?

Q7. Why does a liquid’s surface behave like a stretched membrane?

Q8. Why does the pressure exerted by a fluid increase with depth?

Q9. What is the gauge pressure at a depth of \( 1.9 \, \text{m} \) in ethyl alcohol (\( \rho = 806 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. Why does a mercury barometer use mercury instead of water?