NEET Mechanical Properties of Fluids — Set 12

Question 1

What is the excess pressure inside a mercury drop of radius $ 2 \, \text{mm} $ at $ 20^\circ \text{C} $? (Surface tension of mercury = $ 0.465 \, \text{N/m} $)

Accepted Answer

Excess pressure in a drop: $ \Delta P = \frac{2 S}{r} $. $ S = 0.465 \, \text{N/m} $, $ r = 2 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{2 \times 0.465}{2 \times 10^{-3}} = 465 \, \text{Pa} $.

Question 2

Which statement is incorrect about surface tension?

Accepted Answer

Surface tension arises from cohesive forces at the liquid’s surface, decreasing with temperature due to weaker molecular interactions, not increasing. The incorrect statement is that it increases with temperature.

Question 3

An aircraft ($ m = 2.8 \times 10^5 \, \text{kg} $, wing area $ 480 \, \text{m}^2 $) flies level. What is the pressure difference across the wings? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ \Delta P \cdot A = mg $. $ mg = 2.8 \times 10^5 \times 9.8 = 2.744 \times 10^6 \, \text{N} $, $ A = 480 \, \text{m}^2 $. $ \Delta P = \frac{2.744 \times 10^6}{480} = 5716.67 \, \text{Pa} \approx 5717 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 12

Q1. What is the excess pressure inside a mercury drop of radius \( 2 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension of mercury = \( 0.465 \, \text{N/m} \))

Q2. Which statement is incorrect about surface tension?

Q3. An aircraft (\( m = 2.8 \times 10^5 \, \text{kg} \), wing area \( 480 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. A tank has a hole \( 1.3 \, \text{m} \) below the water surface, open to the atmosphere. What is the efflux speed? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. Why does adding a wetting agent like soap reduce the angle of contact of water on a surface?

Q6. Which of the following statements is correct about the angle of contact?

Q7. What is the total pressure at a depth of \( 1.8 \, \text{m} \) in oxygen liquid (\( \rho = 1.43 \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q8. What is the gauge pressure at \( 2.5 \, \text{m} \) depth in a tank of mercury (\( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. What is the gauge pressure at a depth of \( 2.4 \, \text{m} \) in whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A plate of area \( 0.05 \, \text{m}^2 \) moves at \( 0.7 \, \text{m/s} \) over a \( 0.8 \, \text{mm} \) thick water film (\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \)). What force is required?