Dimensions of Gyromagnetic ratio are

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(B) The gyromagnetic ratio $(\gamma)$ is defined as the ratio of the magnetic dipole moment $(M)$ to the angular momentum $(L)$ of a system.$\gamma =

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$[L^0 M^{-1} T^1 I^1]$

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(B) The gyromagnetic ratio $(\gamma)$ is defined as the ratio of the magnetic dipole moment $(M)$ to the angular momentum $(L)$ of a system.$\gamma = \frac{M}{L}$Since the magnetic moment $M = I \cdot A$ (where $I$ is current and $A$ is area),its dimensions are $[I^1 L^2]$.Since angular momentum $L = mvr$,its dimensions are $[M^1 L^2 T^{-1}]$.Therefore,the dimensions of the gyromagnetic ratio are:$	ext{Dimension} = \frac{[I^1 L^2]}{[M^1 L^2 T^{-1}]} = [M^{-1} L^0 T^1 I^1]$.

List $I$	List $II$
$A$. Spring constant	$I$. $(T^{-1})$
$B$. Angular speed	$II$. $(MT^{-2})$
$C$. Angular momentum	$III$. $(ML^2)$
$D$. Moment of inertia	$IV$. $(ML^2T^{-1})$

Similar Questions

Write the dimensional formula of $\frac{k}{m}$,where $k$ is the spring constant and $m$ is the mass.

Match List $I$ with List $II$:
List $I$ List $II$
$A$. Spring constant $I$. $(T^{-1})$
$B$. Angular speed $II$. $(MT^{-2})$
$C$. Angular momentum $III$. $(ML^2)$
$D$. Moment of inertia $IV$. $(ML^2T^{-1})$

Choose the correct answer from the options given below:

Given below are two statements :
Statement $(I)$ : Dimensions of specific heat are $\left[L^2 \,T^{-2} \,K^{-1}\right]$.
Statement $(II)$ : Dimensions of gas constant are $\left[ML^2 \,T^{-1} \,K^{-1}\right]$.

Which of the following quantities is dimensionless?

Write the dimensional formula for energy density.

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