NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 14

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Question 14.20:

An air chamber of volume has a neck area of cross section into which a ball of mass just fits and can move up and down without any friction. Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal

An air chamber of volume V has a neck area of cross section …

Figure Shown Theair Chamber

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Answer:

Volume of the air chamber

Area of cross)section of the neck

Mass of the ball

The pressure inside the chamber is equal to the atmospheric pressure.

Let the ball be depressed by units. As a result of this depression, there would be a decrease in the volume and an increase in the pressure inside the chamber.

Decrease in the volume of the air chamber,

Volumetric strain

Bulk Modulus of air,

In this case, stress is the increase in pressure. The negative sign indicates that pressure increases with a decrease in volume.

The restoring force acting on the ball,

In simple harmonic motion, the equation for restoring force is:

Where, is the spring constant

Comparing equations we get:

Time period,