Two thin films of same liquid of surface tension 'T' are formed between a smooth rectangular wire frame and two thin uniform strainght wires each of mass 'm' and length 'I' connected to a massless non-deformed spring of stiffness 'k' and then the system is released form rest. The maximum elongation produced in the spring is

Options

A. `(2Tl)/(K)`
B. `(4Tl)/(K)`
C. `(6Tl)/(K)`
D. `(8Tl)/(K)`

Answer

B

Explanation

Force of surface tension on each wire is `F = 2Tl`
`(md^(2)x)/(dt^(2)) = F - 2Kx`
`= -2K (x - (F)/(2K))`
`(d^(2)x)/(dt^(2)) = - (2k)/(m) (x - (F)/(2k))`
`therefore` Amplitude of SHM.
`A = (F)/(2k) = (2Tl)/(2k) = (Tl)/(k)`
`therefore` Maximum elongation produced in the spring is
`Deltal_(max) = 4A = (4Tl)/(k)`