One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.

(i)One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion. Find the time period of oscillation if length of mercury column in the tube is (ii)An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can more up and down without any friction. Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal.

One end of a V-tube containing mercury is connected ot a suction pump and the other end to atmosphere. The two arms of the tube are inclined to horizontal at an angle of 45^(@) each. A small pressure difference is created between two columns when the suction pump is removed. Will Neglect capillary and viscous forces. Find the time period of oscillation.

One end of V-tube containing mercury is connected to a suction grouup and the other end to atmosphere. The two arms of the tube are inclined to horizontal at an angle of 45^(@) each. A small pressure difference is created between two columns when the ssuction pump is removed. Will the column of mercuty in V-tube execute simple harmonic motion? Neglect capillary and viscous forces. Fing the time period of oscillation.

One end a U-tube of unifrom bore (area A) cpmtaining mercury is connected to sunction pump . Because of it the level of liquid of density rho falls in one limb. When the pump is removed, the restoring force in the other limb is

An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the cloumn. The upper end of the tube is open to the atmosphere. the atmosphric pressure equals 76cm of mercury. The lenghts of the mercury column respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of 60^(@) ? Assume the temperature to remain constant.

A pitot tube Fig. is used to determine the air speed of an airplane. It consists of an outer tube with a number of small holes B (four are shown that allow air into the tube, that tube is connected to one arm of a U-tube. The other arm of the U-tube is connected to hole A at the front end of the device, which points in the direction the plane is headed. At A the air becomes stagnant so that v_(A) = 0. At B, however, the speed of the air presumably equals the airspeed v of the plane. (a) Use Bernoulli's equation to show that v = sqrt((2rho gh)/(rho_(air))) where rho is the density of the liquid in the U-tube and his the difference in the liquid levels in that tube. (b) Suppose that the tube contains alcohol and the level difference h is 20.0 cm. What is the plane's speed relative to the air? The density of the air is 1.03 kg//m^(3) and that of alcohol is 810 kg/ m^(3)