An air chamber of volume v has a neck area of cross section a into whicha ball of mass m just fits and can move up and down without any friction. Show that when the ball is pressed down a little and released for the time priod of oscillation, assuming pressure-volume variations of the air to be isothermal.

An air chamber of volume v has a neck area of cross section a into whi

1.	An air chamber of volume v has a neck area of cross section a into whicha ball of mass m just fits and can move up and down without any friction. Show that when the ball is pressed down a little and released for the time priod of oscillation, assuming pressure-volume variations of the air to be isothermal.
Answer» SOLUTION : , volume of chamber = V Area of cross section of neck = a mass of ball = m Intially pressure Let the ball be depressed by y units. Due to depression, there will be reduction in volume and hence, increase of pressure inside chamber. `therefore` Decrease in volume of chamber = `DELTAV = AY` `therefore` Volumetric strain` = (DeltaV)/(V) = (ay)/(V)` `therefore B = Bulk modules= -(P)/((DeltaV)/(V)) = -(PV)/(ay)` `P = -(Bay)/(V)` Restoring force `F = PA` ` = -(Ba^(2)y)/(V)` As `F = -Kx` `therefore` we can write `K = (Ba^(2))/(V)` `T = 2pi sqrt((mV)/(Ba^(2)))`