NEET Mechanical Properties of Fluids — Set 5

Question 1

A capillary tube of radius $ 0.05 \, \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 $)

Accepted Answer

$ h = \frac{2 S \cos \theta}{\rho g a} $. $ S = 0.0727 \, \text{N/m} $, $ \rho = 1000 \, \text{kg/m}^3 $, $ g = 9.8 \, \text{m/s}^2 $, $ a = 0.05 \times 10^{-3} \, \text{m} $. $ h = \frac{2 \times 0.0727 \times 1}{1000 \times 9.8 \times 0.05 \times 10^{-3}} = 0.2967 \, \text{m} = 29.67 \, \text{cm} $.

Question 2

What ensures that a submarine can withstand high pressure at great depths?

Accepted Answer

The submarine’s rigid structure resists the external hydrostatic pressure ($ P = \rho g h $), which increases with depth, preventing collapse by balancing the inward force with structural strength.

Question 3

Why does a barometer reading increase when taken to a lower altitude?

Accepted Answer

At lower altitudes, the air column above is taller and heavier, increasing atmospheric pressure ($ P_a = \rho g h $), which raises the height of the mercury column in the barometer to balance the greater external pressure.

NEET Physics: Mechanical Properties of Fluids — Practice Set 5

Q1. A capillary tube of radius \( 0.05 \, \text{mm} \) 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 \( g = 9.8 \, \text{m/s}^2 \))

Q2. What ensures that a submarine can withstand high pressure at great depths?

Q3. Why does a barometer reading increase when taken to a lower altitude?

Q4. Why does a fluid’s density remain nearly constant in streamline flow through a narrowing pipe?

Q5. A bubble of radius \( 6 \, \text{mm} \) is blown at \( 25 \, \text{cm} \) depth in water (\( \rho = 1000 \, \text{kg/m}^3 \), \( S = 0.0727 \, \text{N/m} \)). What is the total pressure inside? (Take \( P_a = 1.01 \times 10^5 \, \text{Pa} \), \( g = 10 \, \text{m/s}^2 \))

Q6. What is the excess pressure inside a helium drop of radius \( 1 \, \text{mm} \) at \( -270^\circ \text{C} \)? (Surface tension = \( 0.000239 \, \text{N/m} \))

Q7. A soap film supports \( 4.8 \times 10^{-2} \, \text{N} \) over a \( 48 \, \text{cm} \) slider. What is the surface tension?

Q8. A hydraulic lift raises a \( 2000 \, \text{kg} \) load using a small piston of radius \( 5 \, \text{cm} \) and a large piston of radius \( 20 \, \text{cm} \). What force is applied on the small piston? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. What happens to an object falling through a viscous fluid when the viscous force equals the gravitational force?

Q10. A hydraulic system applies \( 180 \, \text{N} \) on a small piston of area \( 0.012 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.06 \, \text{m}^2 \)?

Q11. A pipe’s cross-sectional area decreases from \( 0.15 \, \text{m}^2 \) to \( 0.05 \, \text{m}^2 \). If water flows at \( 1.8 \, \text{m/s} \) in the larger section, what is the speed in the smaller section?

Q12. Water flows through a pipe of area \( 0.05 \, \text{m}^2 \) at \( 1.5 \, \text{m/s} \). What is the speed in a section of area \( 0.015 \, \text{m}^2 \)?

Q13. What is the absolute pressure at \( 250 \, \text{m} \) depth in seawater (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) with \( P_a = 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q14. A swimmer is at a depth of \( 5 \, \text{m} \) in a lake (\( \rho = 1000 \, \text{kg/m}^3 \)). What is the gauge pressure experienced by the swimmer? (Take \( g = 10 \, \text{m/s}^2 \))

Q15. What is the absolute pressure \( 800 \, \text{m} \) deep in an ocean (\( \rho = 1.03 \times 10^3 \, \text{kg/m}^3 \)) with \( P_a = 1.01 \times 10^5 \, \text{Pa} \)? (Take \( g = 9.8 \, \text{m/s}^2 \))