NEET Mechanical Properties of Fluids — Set 17

Question 1

A capillary tube of radius $ 0.2 \, \text{mm} $ is dipped in mercury ($ S = 0.4355 \, \text{N/m} $, $ \rho = 13.6 \times 10^3 \, \text{kg/m}^3 $, $ \cos \theta = -0.5 $). What is the depression? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Capillary rise: $ h = \frac{2 S \cos \theta}{\rho g a} $. $ S = 0.4355 \, \text{N/m} $, $ \rho = 13.6 \times 10^3 \, \text{kg/m}^3 $, $ g = 10 \, \text{m/s}^2 $, $ a = 0.2 \times 10^{-3} \, \text{m} $, $ \cos \theta = -0.5 $. $ h = \frac{2 \times 0.4355 \times (-0.5)}{13.6 \times 10^3 \times 10 \times 0.2 \times 10^{-3}} = -0.016 \, \text{m} = -1.6 \, \text{cm} $.

Question 2

What happens if the pressure applied to a hydraulic system exceeds the fluid’s ability to transmit it?

Accepted Answer

Pascal’s law assumes an incompressible fluid. If pressure exceeds the fluid’s incompressibility limit, the fluid compresses or the system fails (e.g., leaks or bursts), as the assumption of uniform pressure transmission breaks down.

Question 3

What property distinguishes liquids and gases from solids in terms of shape?

Accepted Answer

Liquids and gases are fluids that can flow and take the shape of their container due to their inability to maintain a fixed shape, unlike solids, which have a definite shape due to strong intermolecular forces resisting deformation.

NEET Physics: Mechanical Properties of Fluids — Practice Set 17

Q1. A capillary tube of radius \( 0.2 \, \text{mm} \) is dipped in mercury (\( S = 0.4355 \, \text{N/m} \), \( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \), \( \cos \theta = -0.5 \)). What is the depression? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. What happens if the pressure applied to a hydraulic system exceeds the fluid’s ability to transmit it?

Q3. What property distinguishes liquids and gases from solids in terms of shape?

Q4. Water (\( \rho = 1000 \, \text{kg/m}^3 \)) flows horizontally at \( 3.2 \, \text{m/s} \) with pressure \( 1.85 \times 10^5 \, \text{Pa} \). If the speed increases to \( 5.8 \, \text{m/s} \), what is the new pressure?

Q5. What is the force on a submarine window (\( 0.09 \, \text{m}^2 \)) at \( 200 \, \text{m} \) 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. Which statement is incorrect about capillary action?

Q7. A hydraulic press applies \( 250 \, \text{N} \) on a small piston of area \( 0.02 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.08 \, \text{m}^2 \)?

Q8. Why does the height of a mercury column in a barometer decrease during a storm?

Q9. Which statement is incorrect about fluids?

Q10. A hydraulic press applies \( 350 \, \text{N} \) on a small piston of area \( 0.025 \, \text{m}^2 \). What force is exerted by a large piston of area \( 0.1 \, \text{m}^2 \)?