NEET Mechanical Properties of Fluids — Set 1

Question 1

A sphere of radius $ 0.07 \, \text{m} $ moves at $ 0.14 \, \text{m/s} $ through honey ($ \eta = 0.2 \, \text{Pa s} $). What is the viscous drag force?

Accepted Answer

Stokes’ law: $ F = 6 \pi \eta a v $. $ \eta = 0.2 \, \text{Pa s} $, $ a = 0.07 \, \text{m} $, $ v = 0.14 \, \text{m/s} $. $ F = 6 \times 3.14 \times 0.2 \times 0.07 \times 0.14 = 0.0369 \, \text{N} $.

Question 2

A hydraulic press applies $ 200 \, \text{N} $ on a small piston of area $ 0.01 \, \text{m}^2 $. What force is exerted by a large piston of area $ 0.04 \, \text{m}^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 = 0.01 \, \text{m}^2 $, $ A_2 = 0.04 \, \text{m}^2 $. $ F_2 = 200 \times \frac{0.04}{0.01} = 200 \times 4 = 800 \, \text{N} $.

Question 3

What is the fundamental difference between gauge pressure and absolute pressure?

Accepted Answer

Absolute pressure is the total pressure, including atmospheric pressure ($ P = P_a + \rho g h $), while gauge pressure is the excess pressure above atmospheric pressure ($ P_g = \rho g h $), as defined in the chapter.

NEET Physics: Mechanical Properties of Fluids — Practice Set 1

Q1. A sphere of radius \( 0.07 \, \text{m} \) moves at \( 0.14 \, \text{m/s} \) through honey (\( \eta = 0.2 \, \text{Pa s} \)). What is the viscous drag force?

Q2. A hydraulic press applies \( 200 \, \text{N} \) on a small piston of area \( 0.01 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.04 \, \text{m}^2 \)?

Q3. What is the fundamental difference between gauge pressure and absolute pressure?

Q4. What is the total pressure at a depth of \( 2.8 \, \text{m} \) in whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. A hydraulic lift raises a \( 1900 \, \text{kg} \) load using a small piston of radius \( 4.5 \, \text{cm} \) and a large piston of radius \( 18 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. A soap bubble of radius \( 9 \, \text{mm} \) has a surface tension of \( 0.026 \, \text{N/m} \). What is the excess pressure inside?

Q7. What prevents a fluid from flowing when the pressure gradient is zero?

Q8. A soap bubble of radius \( 12 \, \text{mm} \) has a surface tension of \( 0.024 \, \text{N/m} \). What is the excess pressure inside?

Q9. A soap bubble of radius \( 4 \, \text{mm} \) has a surface tension of \( 0.025 \, \text{N/m} \). What is the excess pressure inside the bubble?

Q10. Water flows at \( 3 \, \text{m/s} \) at \( 2 \, \text{m} \) height with pressure \( 1.3 \times 10^5 \, \text{Pa} \). What is the pressure at \( 0 \, \text{m} \) height with speed \( 4 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 10 \, \text{m/s}^2 \))

Q11. An aircraft (\( m = 2.5 \times 10^5 \, \text{kg} \), wing area \( 500 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q12. A horizontal pipe carries water (\( \rho = 1000 \, \text{kg/m}^3 \)) at \( 2 \, \text{m/s} \) and \( 1.4 \times 10^5 \, \text{Pa} \). If the speed becomes \( 5 \, \text{m/s} \), what is the pressure?

Q13. Water flows at \( 2.0 \, \text{m/s} \) at \( 1.5 \, \text{m} \) height with pressure \( 1.65 \times 10^5 \, \text{Pa} \). What is the pressure at \( 0.2 \, \text{m} \) height with speed \( 3.0 \, \text{m/s} \)? (\( \rho = 1000 \, \text{kg/m}^3 \), \( g = 9.8 \, \text{m/s}^2 \))

Q14. Why does the velocity of a fluid layer in contact with a stationary surface become zero?

Q15. What is the primary reason gases are more compressible than liquids?