Advertisements
Advertisements
Question
A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000 kg/m3 and density of water = 1000 kg/m3.
Advertisements
Solution
Given:
Density of iron, ρI = 8000 kg/m3 = 8 gm/u
Density of water, ρw = 1000 kg/m3 = 1 gm/u
Let x be the external edge of iron.
According to Archemedes' principle,
Weight displaced = Upward thrust
∴ w = u
For the given condition, we have:
Weight of the box = Buoyant force
⇒ V1 ρIg = vρwg
⇒ (x2 × (0.1) × 6) × 8 = x3 × 1 [Volume of iron = v1 = 6 times the volume of each sheet]
⇒ x = 4.8 cm
APPEARS IN
RELATED QUESTIONS
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Angle of contact for the pair of pure water with clean glass is _______.
Explain why Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
Explain why Surface tension of a liquid is independent of the area of the surface
Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2)
The total energy of free surface of a liquid drop is 2π times the surface tension of the liquid. What is the diameter of the drop? (Assume all terms in SI unit).
Define surface tension and surface energy.
Frictional force between solids operates even when they do not move with respect to each other. Do we have viscous force acting between two layers even if there is no relative motion?
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?
A metal piece of mass 160 g lies in equilibrium inside a glass of water. The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg/m3, find the normal force exerted by the bottom of the glass on the metal piece.
A ferry boat has internal volume 1 m3 and weight 50 kg.(a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.(b) If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?
A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9.
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.
Numerical Problem.
A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.
How is surface tension related to surface energy?
Obtain an expression for the surface tension of a liquid by the capillary rise method.
Why coffee runs up into a sugar lump (a small cube of sugar) when one corner of the sugar lump is held in the liquid?
A large number of liquid drops each of radius 'r' coalesce to form a big drop of radius 'R'. The energy released in the process in converted into kinetic energy of the big drop. The speed of the big drop is ______. (T = surface tension of liquid, p = density of liquid)
The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is ______.
Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of the two limbs, of the tube?
[Take surface tension of water T = 7.3 × 10-2 Nm-1, angle of contact = 0, g = 10 ms-2 and density of water = 1.0 × 103 kgm-3]
