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An air chamber of volume V has a neck ar...

An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.14.27). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27].

Text Solution

Verified by Experts

`T=2pisqrt((Vm)/(Ba^(2)))` where B is the bulk modulus of air. For isothermal changes B=P.
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Knowledge Check

  • An air chamber of volume V has a neck area of cross section A into which a ball of mass m just fits and can move up and down without any friction. When the ball is pressed down a little and released, it executes SHM. The time period is assuming pressure, volume variations of air to be isothermal, B = bulk modulus)

    A
    `2pisqrt((Vm)/(A^(2)B))`
    B
    `2pi sqrt((V^(2)m)/(AB))`
    C
    `2pi sqrt((Vm^(2))/(AB))`
    D
    `2pi sqrt((Vm)/(AB^(2)))`
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