The work done to break up a drop of a liquid of radius R and surface tension into eight drops, all of the same size, is
Volume of big drop . If r is the radius of each tiny drop, the total volume of eight drops
Since the total volume remains unchanged, we have
Which gives, . Now, surface area of big drop = .
Total surface area of eight drops =
Increase in surface area .
Work done = surface tension increase in surface area
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the lower and upper surfaces of the wing are v and respectively. If the density of air is and the surface area of the wing is A, the dynamic lift on the wing is given by
A piece of copper having an internal cavity weights 264 g in air and 221 g in water. The density of copper is 8.8 gm–3. What is the volume of the cavity?
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
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
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?
A rectangular tank is filled to the brim with water. When a hole at its bottom is unplugged, the tank is emptied in time T. If the tank is half-filled with water, it will be emptied in time
Two capillary tubes A and B of radii ra and rb and lengths la and lbrespectively are held horizontally. The volume of water flowing per second through tube A is Qa when the pressure difference across its ends is maintained at P. When the same pressure difference is maintained across tube B, the volume of water flowing per second through it is Qb. The ratio is
. If a pressure difference P is maintained across tube A, the rate of flow of water in it is Q. If the tubes are connected in series and the same pressure difference P is maintained across the combination, the rate of flow through the combination will be
If the surface tension of soap solution is , What is the work done in blowing soap bubble of radius r?
A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If is the surface tension of soap solution, the energy spent in doing so is