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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 as shown. When the ball is pressed down a little and released, it executes S.H.M with what time period. (B is bulk modulus of elasticity of air)

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$2 π \sqrt{\frac{B a^{2}}{m V}}$

$\frac{1}{2 π} \sqrt{\frac{B a^{2}}{m V}}$

$2 π \sqrt{\frac{m V}{B a^{2}}}$

$\frac{1}{2 π} \sqrt{\frac{B a}{m V}}$

answer is C.

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Detailed Solution

$B = \frac{(\frac{F}{a})}{- (\frac{Δ V}{V})}$

$F = - B a (\frac{Δ V}{V}) = - B (a) \frac{(a y)}{V}$

$m a' = - \frac{B a^{2}}{V} y$

$ω = \sqrt{\frac{B a^{2}}{m V}}$

$T = 2 π \sqrt{\frac{m V}{B a^{2}}}$

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