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The position (x) of a car varies with time (t) as x = pt2 + qFind the dimensions of p. (Here x is in m, t is in second, p and q are constants)
1. LT-1
2. LT-2
3. L2T-2
4. L-2T

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Correct Answer - Option 2 : LT-2

CONCEPT:

  • Principle of homogeneity of dimensions: According to this principle, a physical equation will be dimensionally correct if the dimensions of all the terms occurring on both sides of the equation are the same.
    • This principle is based on the fact that only the physical quantities of the same kind can be addedsubtracted, or compared.
    • Thus, velocity can be added to velocity but not to force.

EXPLANATION:

Given that:

x = pt2 + q

  • From the principle of dimensional homogeneity, the left-hand side of the equation dimensionally equal to the right-hand side of the equation.
  • The dimension formula of position (x) = [L]

∴ [L] = [p] [T2]

[p] = [LT-2]

  • Therefore the dimensions of 'p' is [LT-2].

For the second term,

⇒ [L] = [q]

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