An air chamber of volume V, has a long of $$cross-sectional$$ area A. A ball of mass m is fitted smoothly in the neck. The bulk modulus of air is B. If the ball is pressed down slightly and released, the time period of its oscillation is

Question

Infinity Learn · Accepted Answer

Let the ball is pressed down by a small amount y, then the value of air decreases by Ay.Then, excess pressure is $$dp=$$−$$BdVV=$$−ByAVA restoring force $$F(Adp)$$ acts in the upward direction.∴     $$F=A$$−$$ByAV=$$−$$BA2V$$⋅y∴     $$a=$$−$$BA2mVy$$ comparing this with $$a=$$−ω$$2y$$⇒    ω$$=BA2mV$$⇒    $$T=2$$πω$$=2$$$$π$$$$mVBA2$$

An air chamber of volume V, has a long of cross-sectional area A. A ball of mass m is fitted smoothly in the neck. The bulk modulus of air is B. If the ball is pressed down slightly and released, the time period of its oscillation is

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