The dimensions of Reynold’s number are
Reynold’s number k is given by the relation
Where vc is the critical velocity of a liquid of density flowing in a tube of radius r. Therefore, the dimensions of k are
Thus, Reynold’s number of dimensionless.
A spring balance reads 10 kg when a bucket of water is suspended from it. What will be the reading of the balance when an iron piece of mass 7.2 kg suspended by a string is immersed with half its volume inside the water in the bucket? Relative density of iron is 7.2.
A vessel contains oil of density 0.8 gcm–3 floating over mercury of density 13.6 gcm–3. A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the sphere in gcm–3 is
A body floats in water with 40% of its volume outside water. When the same body floats in oil, 60% of its volume remains outside oil. The relative density of oil is
The relative density of ice is 0.9 and that of sea water is 1.125. What fraction of the whole volume of an iceberg appears above the surface of the sea?
A common hydrometer has a uniform stem graduated downwards from 0, 1, 2, ….. up to 10. When floating in pure water it reads 0 and in a liquid of relative density 1.5, it reads 10. What is the relative density of a liquid in which it reads 5?
A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker
A cubical vessel of height 1 m is full of water. What is the amount of work done is pumping water out of the vessel? Take g = 10ms–2
The dimensions of viscosity in terms of M, L and T are
A rain drop of radius r falls in air with a terminal speed vt. What is the terminal speed of a rain drop of radius 2r?
Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms–1. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.