Dimensions of Gyromagnetic ratio are

Options

A. `[L^(1)M^(0)T^(1)I^(1)]`
B. `[L^(0)M^(-1)T^(1)I^(1)]`
C. `[L^(1)M^(0)T^(0)I^(-1)]`
D. `[L^(-1)M^(0)T^(1)I^(1)]`

Answer

B

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 " times" ] ) ( ["mass"] ) = ( [A xx T] ) / ( [m] ) `
` rArr [ ( mu )/ ( L ) ] = [ M^ ( - 1 ) L ^( 0 ) T ^( -1) A^( - 1 ) ]" " (because ` Current , I = A )
Hence, the dimension of ` ( ( mu ) / ( L )) ` is ` [ M^( -1 ) L ^ 0 Tl] `