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Explain the principle of homogeneity of ...

Explain the principle of homogeneity of dimensions. What are its uses ? Illustrate by giving one example of each.

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### Step-by-Step Solution **Step 1: Define the Principle of Homogeneity of Dimensions** The principle of homogeneity of dimensions states that in any physical expression or equation, all terms must have the same dimensional formula. This means that when you analyze an equation, each term must be consistent in terms of its dimensions (length, mass, time, etc.). **Step 2: Explain the Importance of Homogeneity** The principle is essential because it ensures that equations are dimensionally consistent, which is crucial for their validity. If the dimensions do not match, the equation is likely incorrect or does not represent a physical reality. ...
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Knowledge Check

  • Using the principle of homogeneity of dimensions, which of the following is correct?

    A
    `T^(2)=(4pi^(2)r^(3))/(GM)`
    B
    `T^(2)=4pi^(2)r^(2)`
    C
    `T^(2)=(4pi^(2)r^(3))/(G)`
    D
    `T=(4pi^(2)r^(3))/(G)`

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