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15 November, 12:33

The volume of an object as a function of time is calculated by v = At3+B:t where t is time measured in seconds and v is in cubic metres. Determine the dimension of the constants A and B.

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  1. 15 November, 12:39
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    A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

    B = m³s = [L³T]

    Explanation:

    We have the equation:

    V = At³ + B/t

    where, the dimensions of each variable are as follows:

    V = m³ = [L]³

    t = s = [T]

    substituting these in equation, we get:

    m³ = A (s) ³ + B/s

    for the homogeneity of the equation:

    A (s) ³ = m³

    A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

    Also,

    B/s = m³

    B = m³s = [L³T]
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