Water is slowly coming out from a vertical pipe. As the water descends after coming out its area of cross section reduces. Explain this on the basis of the equation of continuity.

Water leaks out from an open tank through a hole of area 2mm^2 in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tankis 0.4 m^2 . The pressure at the open surface and the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. a. Find the initial speed of water coming out of the hole. b. Findteh speed of water coming out when half of water has leaked out. c. Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in term of h and dt. d. From the result of part c. find the time required for half of the water to leak out.

The area of cross section of a large tank is 0.5m^2 . It has an opening near the bottom having area of cross section 1cm^2 . A load of 20 kg is applied on the water at the top. Find the velocity of the water coming out of the opening at the time when the height of water level is 50 cm above the bottom. Take g=10ms^-2

2.00 mole of a monatomic ideal gas (U=1.5nRT) is enclosed in an adiabatic, fixed , vertical cylinder fitted with a smooth, light adiabatic piston. The piston is connected to a vertical spring of spring constant 200 N m^(-1) as shown in .the area of cross section of the cylinder is 20.0 cm^(2) . initially, the spring is at its natural length and the temperature of the gas is 300K at its natural length. the atmosphere pressure is 100 kPa. the gas is heated slowly for some time by means of an electric heater so as to move the position up through 10 cm. find (a) the work done by the gas (b) the final temperature of the gas and (c ) the heat supplied by the heater.

A light rod of length 2m is suspended horizontally by means of 2 vertical wires of equal lengths tied to its ends. One of the wire is made of steel & is of cross section A_(1) = 0.1 cm^(2) & other of brass & is of cross section A_(2) = 0.2 cm^(2) , find out the position along the rod at which a weight must be suspended to produce (i) equal stresses in both wires, (ii) equal strains in both wires for steel, y = 20 xx 10^(10)Nm^(-2) & for brass y = 10 xx 10^(10) Nm^(-2) .

When you come out of a river after a dip, you feel cold Explain.

Water flows through a horizontal tube as shown in figure. If the difference of heights of water colun in the vertical tubes is 2 cm and the area of cross section at A and B are 4cm^2 and 2cm^2 respectively, find the rate of flow of water across any section.

A gas is enclosed in a cylindrical vessel fitted with a frictionless piston.the gas is slowly heated for some time. During the process, 10 J of heat is supplied and the piston is found to move out 10cm. Find the increase in the internal energy of the gas, the area of cross section of the cylinder= 4 cm^(2) and the atmospheric pressure =100 kPa.

In guttation water comes out in the form of a liquid from the plant .

A water fountain on the ground sprinkles water all around it. If the speed of the water coming out of the fountain is v. Calculate the total area around the fountain that gets wet.