Question

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.

Answer 1

Restoring force acting on the liquid when suction pump is removed is,

f = – mg ⇒ f = -(A × 2y)ρ × g

where, A = Cross – section area of U tube

ρ = density of liquid

⇒ f = – 2Aρgy

acceleration produced in liquid column

a = f/mass of liquid

Hence it is a SHM.