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A cylindrical piston of mass M slides sm...

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston in distrubed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will (assume T = constant):

A

`T = 2pi sqrt((Mh)/(PA))`

B

`T = 2pi sqrt((MA)/(Ph))`

C

`T = 2pi sqrt((M)/(PAh))`

D

`T = 2pi sqrt(MPhA)`

Text Solution

Verified by Experts

The correct Answer is:
A
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))`
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