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State the principle of homogeneity. Test...

State the principle of homogeneity. Test the dimensional homogeneity of equations—
`s=ut+(1)/(2)at^(2)`

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### Step-by-Step Solution **Step 1: State the Principle of Homogeneity** The principle of homogeneity states that in any dimensional equation, each term on both sides must have the same dimensions. This means that if you have an equation, the dimensions of all terms must be consistent and equal. **Step 2: Identify the Given Equation** ...
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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)`

  • Using the principle of homogeneity of dimensions, find which of the following relation is correct? [T is the period, a is the redius of the orbit and M is the mass of the sun.

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

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