Question

Dimensions of Gyromagnetic ratio are _________.

Options

• [L¹M⁰T¹l¹]

• [L⁰M^-1T¹l¹]

• [L¹M⁰T⁰l^-1]

• [L^-1M⁰T¹l¹]

Answer 1

Dimensions of Gyromagnetic ratio are [L⁰M^-1T¹l¹].

Explanation:

Gyromagnetic ratio is the ratio of magnetic dipole moment of revolving electron to its angular momentum.

i.e., `mu/"L" = "e"/(2"m"_"e")` = gyromagnetic ratio

`[mu/"L"] = (["current" xx "time"])/["mass"]`

`= ["A" xx "T"]/["m"]`

`=> [mu/"L"] = ["M"^-1"L"^0"T"^1"A"^1]`  (∵ Current, I = A)

Hence, the dimension of `(mu/"L") "is" ["M"^-1"L"^0"Tl"]`