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 isremoved, the column of mercury in the U-tube executes simple harmonic motion.

A tunnel is dug through the centre of the earth. Show that a body of mass m when dropped from rest from one end of the tunnel will execute simple harmonic motion.

Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube ? Surface tension of water at the temperature of the experiment is 7.3xx 10^-2 N m^-1 '. Take the angle of contact to be zero and density of water to be 1.0xx 10^3 kg m^- 3 ( g = 9.8 m s^-2 ) .

Two closed vessels of equal volume containing air at pressure P_(1) and temperature T_(1) are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at T_(1) and that in the other at T_(2) , what will be the pressure in the vessels?

Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0xx 10^-3 kg s^-1 , what is the pressure difference between the two ends of the tube ? (Density of glycerine = 1.3xx 10^3 kg m^-3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].

A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom ?

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? motion of an oscillating mercury column in a U-tube.

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?

A open ended mercury manometer is used to measure the pressure exerted by a trapped gas as shown in the figure. Initially manometer shows no difference in mercury level in both columns as shown in diagram. After sparking 'A' dissociates according to following reaction 2A(g)rarr 3B(g)+2C(g) If pressure of Gas "A" dissociates to 0.8 atm, then (Assume temperature to be constant and is 300 K)