NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 12

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Question 14.17:

A simple pendulum of length l and having a bob of mass is suspended in a car. The car is moving on a circular track of radius with a uniform speed. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?

Answer:

The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car.

Acceleration due to gravity

Centripetal acceleration

Where,

is the uniform speed of the car

is the radius of the track Effective acceleration is given as:

Time period,

Where, l is the length of the pendulum

Question 14.18:

Cylindrical piece of cork of density of base area and height floats in a liquid of density . The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period

Where is the density of cork. (Ignore damping due to viscosity of the liquid).

Answer:

Base area of the cork

Height of the cork

Density of the liquid

Density of the cork

In equilibrium:

Weight of the cork Weight of the liquid displaced by the floating cork

Let the cork be depressed slightly by As a result, some extra water of a certain volume is displaced. Hence, an extra up-thrust acts upward and provides the restoring force to the cork.

Up-thrust Restoring force,

Weight of the extra water displaced

through which the cork is depressed

Volume

According to the force law:

Where, is a constant

The time period of the oscillations of the cork:

Where,

Mass of the cork

Volume of the cork Density

Base area of the cork Height of the cork Density of the cork

Hence, the expression for the time period becomes: