NEET Mechanical Properties of Fluids — Set 16

Question 1

A spray tube ($ 9 \, \text{cm}^2 $) has 45 holes of diameter $ 0.6 \, \text{mm} $. If the flow speed is $ 2.0 \, \text{m/min} $, what is the ejection speed?

Accepted Answer

$ A_1 v_1 = A_2 v_2 $, $ v_1 = 2.0 \, \text{m/min} = 0.0333 \, \text{m/s} $, $ A_1 = 9 \times 10^{-4} \, \text{m}^2 $. Hole area: $ A_h = \pi (0.3 \times 10^{-3})^2 $, total $ A_2 = 45 \times \pi \times 9 \times 10^{-8} \approx 1.272 \times 10^{-5} \, \text{m}^2 $. $ v_2 = \frac{9 \times 10^{-4} \times 0.0333}{1.272 \times 10^{-5}} \approx 2.36 \, \text{m/s} $.

Question 2

What is the excess pressure inside a water drop of radius $ 2.5 \, \text{mm} $ at $ 100^\circ \text{C} $? (Surface tension = $ 0.3 \times 10^{-3} \, \text{N/m} $)

Accepted Answer

Excess pressure: $ \Delta P = \frac{2 S}{r} $. $ S = 0.3 \times 10^{-3} \, \text{N/m} $, $ r = 2.5 \times 10^{-3} \, \text{m} $. $ \Delta P = \frac{2 \times 0.3 \times 10^{-3}}{2.5 \times 10^{-3}} = 0.24 \, \text{Pa} $.

Question 3

Which of the following statements is correct about pressure in a fluid at rest?

Accepted Answer

Pressure in a fluid at rest acts equally in all directions (Pascal’s law) and increases with depth ($ P = P_a + \rho g h $), not influenced by the container’s shape, ruling out options involving directionality or shape dependence.

NEET Physics: Mechanical Properties of Fluids — Practice Set 16

Q1. A spray tube (\( 9 \, \text{cm}^2 \)) has 45 holes of diameter \( 0.6 \, \text{mm} \). If the flow speed is \( 2.0 \, \text{m/min} \), what is the ejection speed?

Q2. What is the excess pressure inside a water drop of radius \( 2.5 \, \text{mm} \) at \( 100^\circ \text{C} \)? (Surface tension = \( 0.3 \times 10^{-3} \, \text{N/m} \))

Q3. Which of the following statements is correct about pressure in a fluid at rest?

Q4. A soap film supports \( 2.8 \times 10^{-2} \, \text{N} \) over a \( 56 \, \text{cm} \) slider. What is the surface tension?

Q5. What is the total pressure at a depth of \( 3.2 \, \text{m} \) in water (\( \rho = 1000 \, \text{kg/m}^3 \)) with atmospheric pressure \( 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q6. A \( 45 \, \text{kg} \) person stands on two bones, each with area \( 18 \, \text{cm}^2 \). What is the average pressure on the bones? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q7. A spray tube (\( 5 \, \text{cm}^2 \)) has 25 holes of diameter \( 1.3 \, \text{mm} \). If the flow speed is \( 2.7 \, \text{m/min} \), what is the ejection speed?

Q8. A plate of area \( 0.09 \, \text{m}^2 \) moves at \( 0.5 \, \text{m/s} \) over a \( 0.6 \, \text{mm} \) thick machine oil film (\( \eta = 0.113 \, \text{Pa s} \)). What force is required?

Q9. What is the gauge pressure at a depth of \( 2.7 \, \text{m} \) in mercury (\( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \))? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q10. A hydraulic lift raises a \( 2100 \, \text{kg} \) load using a small piston of radius \( 3.0 \, \text{cm} \) and a large piston of radius \( 12 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 9.8 \, \text{m/s}^2 \))