Advertisements
Advertisements
Question
Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?
Advertisements
Solution
Given:
Depth of the stone from the water surface, h = 500 m
Area of the plane surface of the large stone, A = 2 m2
Density of water, ρw = 103 kgm−3
Force (F) is given by
\[F = P \times A = \left( h \rho_w \times g \right)A \left( P = \text{ Pressure }\right)\]
\[ \Rightarrow \text{ F }= \left( 500 \times {10}^3 \times 10 \right) \times 2\]
\[ = {10}^7 \text{ N/ m}^2\]
The force does not depend on the orientation of the rock when the surface area of the stone remains the same.
APPEARS IN
RELATED QUESTIONS
Derive Laplace’s law for spherical membrane of bubble due to surface tension.
In which of the following substances, surface tension increases with increase in temperature ?
- Copper
- Molten copper
- Iron
- Molten iron
The surface tension of water at 0ºc is 75·5 dyne/cm. Find surface tension of water at 25°C. [ α for water = 0·0021/°C ]
A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
The total free surface energy of a liquid drop is `pisqrt2` times the surface tension of the liquid. Calculate the diameter of the drop in S.l. unit.
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is 30 dyne/cm. (Π = 3.142).
When a glass capillary tube is dipped at one end in water, water rises in the tube. The gravitational potential energy is thus increased. Is it a violation of conservation of energy?
When water droplets merge to form a bigger drop
A capillary tube of radius 0.50 mm is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube 5.0 cm below the surface and the atmospheric pressure. Surface tension of water = 0.075 N m−1.
A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part , find the angle θ made by the water surface in the capillary with the wall.
A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.
Define surface tension.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
Define the angle of contact for a given pair of solid and liquid.
What are the factors affecting the surface tension of a liquid?
Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.
Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Given that the latent heat of vaporisation for water Lv = 540 k cal kg–1, the mechanical equivalent of heat J = 4.2 J cal–1, density of water ρw = 103 kg l–1, Avagadro’s No NA = 6.0 × 1026 k mole–1 and the molecular weight of water MA = 18 kg for 1 k mole.
- Estimate the energy required for one molecule of water to evaporate.
- Show that the inter–molecular distance for water is `d = [M_A/N_A xx 1/ρ_w]^(1/3)` and find its value.
- 1 g of water in the vapor state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state.
- During vaporisation a molecule overcomes a force F, assumed constant, to go from an inter-molecular distance d to d ′. Estimate the value of F.
- Calculate F/d, which is a measure of the surface tension.
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
