Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Derive Laplace’s law for spherical membrane of bubble due to surface tension.
The surface tension of water at 0°C is 75.5 dyne/cm. Calculate surface tension of water at 25°C.
(α for water = 2.7×10-3/°C)
State any two characteristics of the angle of contact
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?
Water near the bed of a deep river is quiet while that near the surface flows. Give reasons.
Why is the surface tension of paints and lubricating oils kept low?
How much amount of work is done in forming a soap bubble of radius r?
Insect moves over the surface of water because of ______.
Explain the phenomena of surface tension on the basis of molecular theory.
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?
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 ______.
The surface tension of the two liquids is respectively 20 and 60 dyne cm-1. The liquids drop from the ends of two tubes of the same radius. The ratio of the weights of the two drops is ______
Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.
Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10–3 Nm–1.
This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 J mole–1K–1, 1 atm. = 1.013 × 105 Pa; the membrane tension is 5 Nm–1.)
A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be ______.
Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.
