NEET Mechanical Properties of Fluids — Set 20

Question 1

A sphere of radius $ 0.015 \, \text{m} $ moves at $ 0.2 \, \text{m/s} $ through water ($ \eta = 1.0 \times 10^{-3} \, \text{Pa s} $). What is the viscous force?

Accepted Answer

Stokes’ law: $ F = 6 \pi \eta a v $. $ \eta = 1.0 \times 10^{-3} \, \text{Pa s} $, $ a = 0.015 \, \text{m} $, $ v = 0.2 \, \text{m/s} $. $ F = 6 \times 3.14 \times 1.0 \times 10^{-3} \times 0.015 \times 0.2 = 5.652 \times 10^{-5} \, \text{N} $.

Question 2

A hydraulic press uses a small piston of area $ 0.008 \, \text{m}^2 $ to exert $ 120 \, \text{N} $. What force is produced by a large piston of area $ 0.032 \, \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 = 120 \, \text{N} $, $ A_1 = 0.008 \, \text{m}^2 $, $ A_2 = 0.032 \, \text{m}^2 $. $ F_2 = 120 \times \frac{0.032}{0.008} = 120 \times 4 = 480 \, \text{N} $.

Question 3

A bubble of radius $ 4 \, \text{mm} $ is formed at $ 50 \, \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 = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ P_i = P_a + \rho g h + \frac{2 S}{r} $. $ P_a = 1.01 \times 10^5 \, \text{Pa} $, $ \rho g h = 1.2 \times 10^3 \times 9.8 \times 0.5 = 5880 \, \text{Pa} $. $ \frac{2 S}{r} = \frac{2 \times 0.025}{4 \times 10^{-3}} = 12.5 \, \text{Pa} $. $ P_i = 1.01 \times 10^5 + 5880 + 12.5 = 1.06892 \times 10^5 \, \text{Pa} $.

NEET Physics: Mechanical Properties of Fluids — Practice Set 20

Q1. A sphere of radius \( 0.015 \, \text{m} \) moves at \( 0.2 \, \text{m/s} \) through water (\( \eta = 1.0 \times 10^{-3} \, \text{Pa s} \)). What is the viscous force?

Q2. A hydraulic press uses a small piston of area \( 0.008 \, \text{m}^2 \) to exert \( 120 \, \text{N} \). What force is produced by a large piston of area \( 0.032 \, \text{m}^2 \)?

Q3. A bubble of radius \( 4 \, \text{mm} \) is formed at \( 50 \, \text{cm} \) 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 \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 9.8 \, \text{m/s}^2 \))

Q4. A \( 1500 \, \text{kg} \) car is lifted by a hydraulic system with a small piston of radius \( 6 \, \text{cm} \) and a large piston of radius \( 18 \, \text{cm} \). What force is needed on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. What is the force on a submarine window (\( 0.06 \, \text{m}^2 \)) at \( 400 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)), interior at atmospheric pressure? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. A spray tube (\( 7 \, \text{cm}^2 \)) has 35 holes of diameter \( 0.8 \, \text{mm} \). If the flow speed is \( 3.0 \, \text{m/min} \), what is the ejection speed?

Q7. Why does the viscosity of liquids generally decrease with increasing temperature?

Q8. What is the primary reason a sharp needle pierces the skin more easily than a blunt object with the same force?

Q9. What is the excess pressure inside a mercury drop of radius \( 4 \, \text{mm} \) at \( 20^\circ \text{C} \)? (Surface tension = \( 0.4355 \, \text{N/m} \))

Q10. Which statement is incorrect about dynamic lift?