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Dimensions and Derivation of Time Period - Testbook.com

Last Updated on Jul 31, 2023

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How to Determine the Dimensional Formula of Time Period
Time period is a fundamental concept in physics, which can be dimensionally represented. But how exactly is this done? Let's break it down.
The dimensional formula of a Time Period is denoted as:
[M⁰ L⁰ T¹]
Here's what each symbol stands for:

M = Mass

L = Length

T = Time

Let's take an example to understand this better. Consider the time period (T) of a simple pendulum, which is given by the formula: T = 2× π × √(L/g)

In this formula, L represents the length of the string and g stands for the Acceleration due to gravity.

The dimensional formula of length is given by [M⁰ L¹ T⁰], and the dimensional formula of acceleration due to gravity is [M⁰ L¹ T^-2].

By substituting these values into the original formula for time period, we arrive at:

T = √[M⁰ L¹ T⁰] × [M⁰ L¹ T^-2]^-1 = √[T²] = [M⁰ L⁰ T¹].

So, the time period is dimensionally represented as [M⁰ L⁰ T¹].

Now that you've got the hang of it, why not explore more dimensional formulas? Here are a few to get you started:

The dimensional formula of Time Period is [M^0 L^0 T^1].

Time Period is derived from the formula T = 2× π × √(L/g), where L is the length of the string and g is the acceleration due to gravity.

The Time Period is dimensionally represented as [M^0 L^0 T^1].

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