Given that "mass" multiply by constant “k” is equal to "energy" divided by “height”. Determine, by using dimensions of each, which physical quantity is
represented by “k”?

K must be an acceleration

Explanation:

Recall that unit of energy consists the following dimensions:

mass * length^2 / time^2

then if we have :  mass * K = energy / length

then the units of K can be obtained by replacing the units of energy by (mass * length^2 / time^2), and then dividing by units of mass:

K = (mass * length^2 / time^2)/ (length * mass)

where we cancel out units of mass, and one unit of length resulting in units of length divided units of time squared. and such are units of acceleration. Therefore K must be an acceleration.

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