NEET Mechanical Properties of Fluids — Set 2

Question 1

A plate of area $ 0.06 \, \text{m}^2 $ moves at $ 0.6 \, \text{m/s} $ over a $ 0.4 \, \text{mm} $ thick glycerine film ($ \eta = 0.83 \, \text{Pa s} $). What force is required?

Accepted Answer

Viscous force: $ F = \eta \frac{v A}{l} $. $ \eta = 0.83 \, \text{Pa s} $, $ v = 0.6 \, \text{m/s} $, $ A = 0.06 \, \text{m}^2 $, $ l = 0.4 \times 10^{-3} \, \text{m} $. $ F = 0.83 \times \frac{0.6 \times 0.06}{0.4 \times 10^{-3}} = 0.83 \times 90 = 74.7 \, \text{N} $.

Question 2

A soap film supports $ 3.6 \times 10^{-2} \, \text{N} $ over a $ 60 \, \text{cm} $ slider. What is the surface tension?

Accepted Answer

$ S = \frac{F}{2 l} $. $ F = 3.6 \times 10^{-2} \, \text{N} $, $ l = 0.6 \, \text{m} $. $ S = \frac{3.6 \times 10^{-2}}{2 \times 0.6} = 0.03 \, \text{N/m} $.

Question 3

A hydraulic system applies $ 150 \, \text{N} $ on a small piston of area $ 0.015 \, \text{m}^2 $. What force is exerted by a large piston of area $ 0.075 \, \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 = 150 \, \text{N} $, $ A_1 = 0.015 \, \text{m}^2 $, $ A_2 = 0.075 \, \text{m}^2 $. $ F_2 = 150 \times \frac{0.075}{0.015} = 150 \times 5 = 750 \, \text{N} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 2

Q1. A plate of area \( 0.06 \, \text{m}^2 \) moves at \( 0.6 \, \text{m/s} \) over a \( 0.4 \, \text{mm} \) thick glycerine film (\( \eta = 0.83 \, \text{Pa s} \)). What force is required?

Q2. A soap film supports \( 3.6 \times 10^{-2} \, \text{N} \) over a \( 60 \, \text{cm} \) slider. What is the surface tension?

Q3. A hydraulic system applies \( 150 \, \text{N} \) on a small piston of area \( 0.015 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.075 \, \text{m}^2 \)?

Q4. What is the excess pressure inside an ethanol drop of radius \( 1.5 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.0227 \, \text{N/m} \))

Q5. Which statement is incorrect about hydraulic systems?

Q6. An aircraft (\( m = 3.0 \times 10^5 \, \text{kg} \), wing area \( 450 \, \text{m}^2 \)) flies level. What is the pressure difference across the wings? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 2.8 \, \text{m/s} \) with pressure \( 1.9 \times 10^5 \, \text{Pa} \). If the speed increases to \( 5.2 \, \text{m/s} \), what is the new pressure?

Q8. Which of the following statements is correct about the equation of continuity?

Q9. A soap bubble of radius \( 15 \, \text{mm} \) has a surface tension of \( 0.023 \, \text{N/m} \). What is the excess pressure inside?

Q10. What property of a fluid does the coefficient of viscosity measure?

Q11. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 4.5 \, \text{m/s} \) with pressure \( 2.0 \times 10^5 \, \text{Pa} \). If the speed increases to \( 7.0 \, \text{m/s} \), what is the new pressure?

Q12. A manometer with seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) shows a height difference of \( 0.19 \, \text{m} \). What is the pressure difference? (Take \( g = 10 \, \text{m/s}^2 \))

Q13. A capillary tube of radius \( 0.55 \, \text{mm} \) is dipped in water (\( S = 0.0727 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. What is the excess pressure inside an oxygen drop of radius \( 0.5 \, \text{mm} \) at \( -183^\circ \text{C} \)? (Surface tension = \( 0.0132 \, \text{N/m} \))

Q15. What is the gauge pressure at a depth of \( 4.5 \, \text{m} \) in ethyl alcohol (\( \rho = 806 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))