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A cylinder piston of mass M sides smooth...

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

A

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

B

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

C

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

D

`T = 2 pi sqrt( MP hA)`

Text Solution

Verified by Experts

The correct Answer is:
A
Consider the process is isothermal
`P_(1) V_(1) = P_(2) V_(2)`
`PV = (P + Delta P) (V - Delta V)`
`rArr PV + Delta PV - PDelta V - Delta P Delta V`
`rArr Delta PV - PDelta V = 0` [neglecting `Delta P Delta V`]
`rArr Delta P (Ah) = P (Ax) rArr Delta P = (P x)/( h)`
Restoring force (F) ` = - Delta PA = ( - P A x)/( h)`
`a = - ((PA)/( hM)) x`
`:. omega = sqrt(( AP)/( Mh)) rArr T = 2 pi sqrt(( Mh)/( PA))`
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