An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. Atmospheric pressure is p 0 and when the piston is in equilibrium, the volume of the gas is V 0 . The piston is now displaced slightly from its equilibrium position. Assuming that the system, is completely isolated from, its surroundings, what is the frequency of oscillation.

f = 1 2 π γ p 0 A 2 + MgA V 0 M

f ⁡ = 1 2 π 1 γ p 0 A 2 + Mg A V 0 M

f ⁡ = 1 2 π p 0 A 2 + Mg A V 0 M

f ⁡ = 1 2 π A p 0 A + Mg A V 0 M

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A ring of mass $m$ is pivoted at a point on its periphery and free to oscillates in vertical plane. A particle of same mass is attached at the lowest point of the ring then time period of small oscillations is

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A ring of mass $m$ is pivoted at a point on its periphery and free to oscillates in vertical plane. A particle of same mass is attached at the lowest point of the ring then time period of small oscillations is