1.

A rectangular pipe having cross sectional area A. It is closed at one end and at its other end ablock having same cross-section and mass 'm' is placed such that system is air tight. Inequilibrium position of block the pressure and volume of air enclosed in pipe are P and Vrespectively. If block is displaced by small distance x inward and released then find the timeperiod of S.H.M. [Assume the walls are frictionless and compression of air is isothermal].

Answer»

`T = 2pi ((mV)/(PA ^(2)))^(1//2)`
`T =(PI)/(2) ((mV)/(PA ^(2)))^(1//2)`
`T = pi (((PA ^(2)))/(mV))^(1//2)`
`T =2pi ((2mv)/(PA ^(2)))^(1//2)`

Solution :
`PV =C `
`PdV +Vdp=0`
`dP =(-P)/(V) dV`
`dp = (-P)/(V) (Ax)`
`implies F _(net) =(dP) A=- ((pa^(2))/(V))X`
`implies F =-kx`


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