NEET Mechanical Properties of Fluids — Set 13

Question 1

Why does the pressure at the bottom of three differently shaped vessels connected at the base remain the same when filled with water to the same height?

Accepted Answer

The hydrostatic paradox demonstrates that pressure in a fluid at rest depends only on depth ($ \rho g h $) and not on the shape or volume of the container. At the same depth, the pressure is identical regardless of the vessel’s shape.

Question 2

An aircraft ($ m = 2.0 \times 10^5 \, \text{kg} $, wing area $ 400 \, \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 = 2.0 \times 10^5 \times 9.8 = 1.96 \times 10^6 \, \text{N} $, $ A = 400 \, \text{m}^2 $. $ \Delta P = \frac{1.96 \times 10^6}{400} = 4900 \, \text{Pa} $.

Question 3

A soap bubble of radius $ 7 \, \text{mm} $ has a surface tension of $ 0.028 \, \text{N/m} $. What is the excess pressure inside?

Accepted Answer

Excess pressure in a bubble: $ \Delta P = \frac{4 S}{r} $. $ S = 0.028 \, \text{N/m} $, $ r = 7 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{4 \times 0.028}{7 \times 10^{-3}} = 16 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 13

Q1. Why does the pressure at the bottom of three differently shaped vessels connected at the base remain the same when filled with water to the same height?

Q2. An aircraft (\( m = 2.0 \times 10^5 \, \text{kg} \), wing area \( 400 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q3. A soap bubble of radius \( 7 \, \text{mm} \) has a surface tension of \( 0.028 \, \text{N/m} \). What is the excess pressure inside?

Q4. A plate of area \( 0.08 \, \text{m}^2 \) moves at \( 0.8 \, \text{m/s} \) over a \( 0.7 \, \text{mm} \) thick glycerine film (\( \eta = 0.83 \, \text{Pa s} \)). What force is required?

Q5. A sphere of radius \( 0.04 \, \text{m} \) moves at \( 0.12 \, \text{m/s} \) through honey (\( \eta = 0.2 \, \text{Pa s} \)). What is the viscous drag force?

Q6. Which of the following statements is correct about terminal velocity?

Q7. A hydraulic lift raises a \( 1600 \, \text{kg} \) load using a small piston of radius \( 4 \, \text{cm} \) and a large piston of radius \( 16 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. What ensures that a fluid at rest cannot sustain a shear stress?

Q9. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 4 \, \text{m/s} \) with pressure \( 1.6 \times 10^5 \, \text{Pa} \). If the speed increases to \( 7 \, \text{m/s} \), what is the new pressure?

Q10. A manometer with mercury (\( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \)) shows a height difference of \( 0.25 \, \text{m} \). What is the pressure difference? (Take \( g = 9.8 \, \text{m/s}^2 \))