The frequency `(n)` of vibration of a string is given as ` n = (1)/( 2 l) sqrt((T)/(m))` , where `T` is tension and `l` is the length of vibrating string , then the dimensional formula is

Options

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

Answer

C

Explanation

`n = (1)/( 2l) sqrt((T)/(m)) rArr n^(2) = (1)/( 4l^(2)) (T)/(m)`
` m = (T) / ( 4 l^(2) n^(2)) = [ (MLT^(-2))/( L^(2) xx T^(-2))] = [ML^(-1)]`