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Chapter 2: Problem 8

The time taken by the bob of a simple pendulum of time period \((\mathrm{T})\) to move from one extreme position to other extreme position is equal to _

Short Answer

Expert verified
Answer: The time taken by the bob to move from one extreme position to the other extreme position is equal to half of its time period (T/2).

Step by step solution

01

Understand the Oscillation of a Simple Pendulum

A simple pendulum consists of a mass (bob) attached to a string of fixed length. The pendulum oscillates back and forth around its equilibrium position through an arc. One complete oscillation, from one extreme position to the other and back to the starting point, is known as the time period (T) of the pendulum.
02

Identify Known and Unknown Variables

In this problem, we are given the time period (T) of the simple pendulum and asked to find the time taken by the bob to move from one extreme position to other extreme position. Known variables: - Time period (T) Unknown variables: - Time taken by the bob to move from one extreme position to other extreme position (t)
03

Relate Known Variables with Unknown Variables

The time taken by the bob to move from one extreme position to the other extreme position is equal to half its time period (T/2). This is because the pendulum takes the same amount of time to move from its equilibrium position to either extreme position and then return. Therefore, we can write the equation: t = T/2
04

Solve the Equation for Requested Time

Now that we have the equation t = T/2, we can directly solve it to find the time taken by the bob to move from one extreme position to the other extreme position. The time taken by the bob to move from one extreme position to other extreme position is equal to (T/2).

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