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16 January, 04:36

A displacement is related to time as x = A sin (2? ft), where A and f are constants. Find the dimensions of A. [Hint: A trigonometric function appearing in an equation must be dimensionless.]

A. L * T

B. L / T

C. L

D. T / L

E. T

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Answers (1)
  1. 16 January, 07:56
    0
    The right option is C. i. e L

    Explanation:

    Dimension of a quantity is the collection of the indexes of each of the fundamental quantities contained in it.

    Therefore, to get the dimension of A in the equation

    X=Asin (2 (pi) ft)

    Making A the subject of the formula

    A = X / (sin (2 (pi) ft)

    Since sin (2 (pi) ft which is a trigonometric function does not have a dimension

    A = L

    The dimension of A is L
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