A tank with a square base of area 2.0 m2 is divided into two compartments by a vertical partition in the middle. There is a small hinged door of face area 20 cm2 at the bottom of the partition. Water is filled in one compartment and an acid of relative density 1.5 in the other, both to a height of 4 m. If g = 10 ms–2, the force necessary to keep to door closed is
Lateral pressure exerted by water on the face of the door in contact with water is
Lateral pressure exerted by acid on the face of the door in contact with acid is
Net pressure on the door .
Now, the face area of the door = 20 cm2
Force on the door = pressure area
Hence, a face of 40 N must be applied on the door in order to counterbalance the force due to the two liquids.
A glass capillary sealed at the upper end is of length 0.11 m and internal diameter . The tube is immersed vertically into a liquid of surface tension . To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same? What will happen to the water level inside the capillary if the seal is now broken?
A conical glass tube of length 0.1 m has diameters 10–3 and at the ends. When it is just immersed in a liquid at 0oC with larger diameter in contact with it, the liquid rises to in the tube. If another cylindrical glass capillary tube B is immersed in the same liquid at 0oC, the liquid rises to height. The rise of liquid in the tube B is only when the liquid is at 50oC. Find the rate at which the surface tension changes with temperature considering the change to be linear. The density of the liquid is and angle of contact is zero. Effect of temperature on density of liquid and glass is negligible.
A rectangular container with base contains 5 kg of water. What is the pressure exerted by water at the bottom of the container?
A cylindrical jar of cross-sectional area 0.01 m2 is filled with water to a height of 50 cm. It carries a tight-fitting piston of negligible mass. What is the pressure at the bottom of the jar when a mass 1 kg is placed on the piston? Take g = 10 ms–2.
A hydraulic lift is used to lift a car of mass 3000 kg. The cross-sectional area of the lift on which the car is supported is . What is the pressure on the smaller piston, if both the pistons are at the same horizontal level?
Take g =10 ms–2.
A spherical ball of radius and 104 kg/m3 falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. The viscosity of water is .
A ring is cut from a platinum tube of 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in a glass vessel. What is the surface tension of water is an extra 3.97 g weight is required to pull it away from water? (g = 980 cm/s2)
What is the pressure on the smaller piston if the bigger piston is 5 m above the smaller piston. The density of oil filling the hydraulic machine is 800 kg m–3.
A vertical off-shore structure is built to withstand a maximum stress of 108Pa. The structure is suitable for putting up on the top of an oil well in Bombay High at a location where the depth of the sea is less than
(Take g = 10 ms–2 and density of sea water = 1000 kgm–3)
A cubical block of steel of each side equal to l is floating on mercury in a vessel. The densities of steel and mercury are and . The height of the block above the mercury level is given by