Question

What is the period of a simple pendulum 50 cm long on earth and in a freely falling elevator?

Answer 1

Concepts and reason

The concept used to solve the question is the simple harmonic motion.

Latter determine the period of a pendulum on the earth and elevator by using the expression of the period of a pendulum.

Fundamentals

Simple harmonic motion:

The simple harmonic motion is defined as when an object moves to and fro motion along a line that motion of the object is called simple harmonic motion. The time taken to complete one osculation is known as a period.

The period of the pendulum in simple harmonic motion is mathematically defined as,

Here, is the period of the pendulum is the length of the pendulum and acceleration under which pendulum is moving.

The period of the pendulum in simple harmonic motion when it moves under gravitational acceleration is defined as,

Here, is the acceleration due to gravity.

Substitute for and for in above expression as

The period of the pendulum in simple harmonic motion when it moves on the elevator is defined as,

Here, is the acceleration of the elevator.

Substitute for and for in above expression as

Ans:

The period of the pendulum when it moves on earth is.

The period of the pendulum when it moves on the elevator is.