Two identical cylindrical vessels, each of base area A, have their bases at the same horizontal level. They contain a liquid of density . In one vessel the height of the liquid is h1 and in the other h2 > h1. When the two vessels are connected, the work done by gravity in equalizing the levels is
After the levels in the two vessels becomes equal, the increase in height of the liquid in one vessel is with the same decrease in height in the other. Thus, effectively a slab of liquid in thickness falls a vertical distance equal to its thickness under the action of gravity.
Work done by the gravity is
Where mass of slab m is given by
The dimensions of viscosity in terms of M, L and T are
The dimensions of Reynold’s number 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.
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A stone of relative density k is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of
A cylindrical jar has radius r. To what height h should it be filled with a liquid so that the force exerted by the liquid on the sides of the jar equals the force exerted on the bottom?