A cylinder piston of mass `M` sides smoothly inside a long cylinder closed at and enclosing a certain mass of gas The cylinder is kept with its axis horizontal if the piston is distanced from its equations positions it oscillation simple harmonically .The period of oscillation will be

Options

A. `T = 2pi sqrt((Mh)/(PA))`
B. `T = 2pi sqrt((MA)/(Ph))`
C. `T = 2pi sqrt((M)/(PAh))`
D. `T = 2pi sqrt(MPhA)`

Answer

A

Explanation

So extra force acting on the piston is given by

`F = - ((P Delta v)/(v)) A`
`F = -(P.(Ax))/((A.h)) .A`
`alpha = - omega^(2)x`
where `omega^(2) = ((PA)/(Mh))`
`rArr omega = sqrt((PA)/(ML))`
`:. T = (2pi)/(omega) = 2pi sqrt((Mh)/(PA))`