Question

The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of ______.

Options

• angular momentum

• velocity

• frequency

• time

Answer 1

The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of frequency.

Explanation:

The dimensions of Planck's constant,

[h] = `(["E"])/(["v"]) = (["ML"^2 "T"^-2])/(["M"^0 "L"^0 "T"^-1]) = ["ML"^2 "T"^-1]`

and that moment of inertia,

[I] = [M][R]² = [M][L]² = [ML² T⁰]

`therefore (["h"])/(["l"]) = (["ML"^2 "T"^-1])/(["ML"^2 "T"^0]) = ["T"^-1]` = [v]

Thus, the ratio of dimensions of Planck's constant to that at moment of inertia is the dimensions of frequency.