JEE Main 2013PhysicsOscillationsHardMCQ

JEE Main 2013 — Oscillations Question with Solution

JEE Main 2013 (07 Apr)

Question

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is M0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

Choose an option

Show full solutionCorrect option: A
Correct answer
A12πA2γP0MV0.

Step-by-step explanation

For an adiabatic process,

Pvγ=constant

Differentiating with respect to v,

dPdvvγ+Pγvγ-1=0

dP=-γPvdv=-γPvAdx



Thus, the acceleration, a=dFM=γPA2MVdx

Comparing with ,  a=-ω2dx, we get,

ω=γP0A2MV0=2πf

f=12πγP0A2MV0

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About this question

This is a previous-year question from JEE Main 2013, covering the Oscillations chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.