SHMHard

Question

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end as shown in figure enclosing a certain mass of a gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be (process is isothermal)

Options

A.
B.
C.
D.

Solution


force  = (P − P0) A = Ma
by P1V1 = P2V2
P0hA = P(h − x) A    ⇒ P =
So force = = a
a = ; (for small x)
T = 2π

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