Motion of an oscillating liquid column in a U-tube is

Options

A. Periodic but not simple harmonic
B. non-periodic
C. simple haromic and time period is independent of the density of the liquid
D. simple harmonic and time period is directly proportional to the density of the liquid

Answer

C

Explanation

Restoring force `F =` Weight of liquid column of height `2y`
`F =- (A xx 2y + rhp) xxg =-2A rho gy`
`F alpha -y`
Motion is `SHM` with force constant
`K = 2A rho g`
`rArr` Timeperiod `T = 2pi sqrt((m)/(k))`
`= 2pi sqrt((A xx 2h xx rho)/(2A rhog)) = 2pi sqrt((h)/(g))`
which is independent of the density of the liquid.