﻿ An air chamber of volume V has a neck of cross-sectional area a into which a light ball of mass m can move without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air in B, the time period of the resulting oscillation of the ball is given by  : Kaysons Education

# An Air Chamber Of Volume V has A Neck Of Cross-sectional Area A Into Which A Light Ball Of Mass m can Move Without Friction. The Diameter Of The Ball Is Equal To That Of The Neck Of The Chamber. The Ball Is Pressed Down A Little And Released. If The Bulk Modulus Of Air In B, The Time Period Of The Resulting Oscillation Of The Ball Is Given By

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## Question

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Let P be the pressure of air in the chamber. When the ball is pressed down a distance x, the volume of air decreased from V to say V – âˆ†V. Hence the pressure increases from P to P + âˆ†P. The change in volume (see fig) is

The excess pressure âˆ†P is related to the bulk modulus B

now restoring force on ball = excess pressure × cross-sectional area

Hence the motion of the ball is simple harmonic. If m is the mass of the ball, the time period of the SHM is

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