Which of these equations is dimensionally correct? I. mv/ t= F II. xv^2= Fx^3/ x^2 III. xt= vt^2+at^3

Question

Which of these equations is dimensionally correct?
I. mv/ t= F
II. xv^2= Fx^3/ x^2
III. xt= vt^2+at^3

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Vân Khánh 2 months 2021-07-30T21:55:16+00:00 1 Answers 4 views 0

Answers ( )

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    2021-07-30T21:57:11+00:00

    Answer: first and third.

    Explanation:

    An equation is dimensionally correct if the units are the same in both sides of the equation.

    first, let’s define the units used:

    {m} = kg

    {v} = m/s

    {F} = kg*m/s^2

    {x} = m

    {t} = s

    {a} = m/s^2

    Now, let’s analyze each option:

    1) m*v/t = F

    in the left side the units are:

    {m}*{v}/{t} =  kg*(m/s)*(1/s) = kg*m/s^2

    And as is written above, these are the units of F, so this is correct.

    2) x*v^2 = F*(x^3/x^2)

    This is more trivial, in the right side we can see an F, that has mass units (kg)  and in the left side we have x and v, and we know that none of these have mass units, so this expression is not correct.

    3) xt= vt^2+at^3

    the units in the right side are:

    {x}*{t] = m*s

    in the right side are:

    {v}*{t}^2 + {a}*{t}^2 = (m/s)*s^2 + (m/s^2)*s^3 = m*s + m*s

    So in both sides of the equation we have the same units, then this equation is dimensionally correct.

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