NEET Mechanical Properties of Fluids — Set 3

Question 1

A hydraulic lift raises a $ 1400 \, \text{kg} $ load using a small piston of radius $ 2.5 \, \text{cm} $ and a large piston of radius $ 10 \, \text{cm} $. What force is applied on the small piston? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ F_1 = \frac{A_1}{A_2} F_2 $, $ F_2 = 1400 \times 9.8 = 13720 \, \text{N} $. $ A_1 = \pi (0.025)^2 $, $ A_2 = \pi (0.1)^2 $, $ \frac{A_1}{A_2} = \frac{0.000625}{0.01} = \frac{1}{16} $. $ F_1 = \frac{13720}{16} = 857.5 \, \text{N} \approx 858 \, \text{N} $.

Question 2

A capillary tube of radius $ 0.35 \, \text{mm} $ is dipped in ethanol ($ S = 0.0227 \, \text{N/m} $, $ \rho = 806 \, \text{kg/m}^3 $, $ \cos \theta = 1 $). What is the capillary rise? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

$ h = \frac{2 S \cos \theta}{\rho g a} $. $ S = 0.0227 \, \text{N/m} $, $ \rho = 806 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $, $ a = 0.35 \times 10^{-3} \, \text{m} $. $ h = \frac{2 \times 0.0227 \times 1}{806 \times 10 \times 0.35 \times 10^{-3}} = 0.0161 \, \text{m} = 1.61 \, \text{cm} $.

Question 3

A spray tube ($ 6 \, \text{cm}^2 $) has 30 holes of diameter $ 1.1 \, \text{mm} $. If the flow speed is $ 3.6 \, \text{m/min} $, what is the ejection speed?

Accepted Answer

$ A_1 v_1 = A_2 v_2 $, $ v_1 = 3.6 \, \text{m/min} = 0.06 \, \text{m/s} $, $ A_1 = 6 \times 10^{-4} \, \text{m}^2 $. Hole area: $ A_h = \pi (0.55 \times 10^{-3})^2 $, total $ A_2 = 30 \times \pi \times 3.025 \times 10^{-7} \approx 2.851 \times 10^{-5} \, \text{m}^2 $. $ v_2 = \frac{6 \times 10^{-4} \times 0.06}{2.851 \times 10^{-5}} \approx 1.26 \, \text{m/s} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 3

Q1. A hydraulic lift raises a \( 1400 \, \text{kg} \) load using a small piston of radius \( 2.5 \, \text{cm} \) and a large piston of radius \( 10 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q2. A capillary tube of radius \( 0.35 \, \text{mm} \) is dipped in ethanol (\( S = 0.0227 \, \text{N/m} \), \( \rho = 806 \, \text{kg/m}^3 \), \( \cos \theta = 1 \)). What is the capillary rise? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A spray tube (\( 6 \, \text{cm}^2 \)) has 30 holes of diameter \( 1.1 \, \text{mm} \). If the flow speed is \( 3.6 \, \text{m/min} \), what is the ejection speed?

Q4. A bubble of radius \( 4.0 \, \text{mm} \) is blown at \( 60 \, \text{cm} \) depth in a soap solution (\( \rho = 1.2 \times 10^3 \, \text{kg/m}^3 \), \( S = 0.025 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 10 \, \text{m/s}^2 \))

Q5. A soap bubble of radius \( 10 \, \text{mm} \) has a surface tension of \( 0.025 \, \text{N/m} \). What is the excess pressure inside?

Q6. What is the gauge pressure at a depth of \( 0.9 \, \text{m} \) in whole blood (\( \rho = 1.06 \times 10^3 \, \text{kg/m}^3 \))? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 3.8 \, \text{m/s} \) with pressure \( 1.8 \times 10^5 \, \text{Pa} \). If the speed increases to \( 6.2 \, \text{m/s} \), what is the new pressure?

Q8. What causes a liquid to form a concave meniscus in a glass tube?

Q9. A capillary tube of radius \( 0.45 \, \text{mm} \) 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 \( g = 9.8 \, \text{m/s}^2 \))

Q10. A capillary tube of radius \( 0.1 \, \text{mm} \) is dipped in water (\( S = 0.073 \, \text{N/m} \), \( \rho = 1000 \, \text{kg/m}^3 \)). What is the height of capillary rise? (Take \( g = 10 \, \text{m/s}^2 \), \( \cos \theta = 1 \))

Q11. A soap bubble of radius \( 7 \, \text{mm} \) has an excess pressure of \( 20 \, \text{Pa} \) inside. What is its surface tension?

Q12. A \( 60 \, \text{kg} \) person stands on two cylindrical bones, each of cross-sectional area \( 15 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 10 \, \text{m/s}^2 \))

Q13. Which of the following statements is correct regarding Pascal’s law?

Q14. A hydraulic system applies \( 300 \, \text{N} \) on a small piston of area \( 0.015 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.045 \, \text{m}^2 \)?

Q15. A soap bubble of radius \( 8 \, \text{mm} \) has a surface tension of \( 0.026 \, \text{N/m} \). What is the excess pressure inside?