## Question

An air chamber of volume *V* has a neck of cross-sectional area a into which a light ball of mass *m* can move without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air in B, the time period of the resulting oscillation of the ball is given by

### Solution

Let *P* be the pressure of air in the chamber. When the ball is pressed down a distance *x*, the volume of air decreased from *V* to say *V* – âˆ†*V*. Hence the pressure increases from *P* to *P* + âˆ†*P*. The change in volume (see fig) is

The excess pressure âˆ†*P* is related to the bulk modulus *B*

now restoring force on ball = excess pressure × cross-sectional area

Hence the motion of the ball is simple harmonic. If *m* is the mass of the ball, the time period of the SHM is

#### SIMILAR QUESTIONS

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_{l}
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