The frequency of vibration of string is given by `v = (p)/(2 l) [(F)/(m)]^(1//2)`. Here `p` is number of segment is the string and `l` is the length. The dimension formula for `m` will be

Options

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

Answer

C

Explanation

`v=(P)/(2l)[F/m]^(1/2) P rarr` number of segments , `l rarr ` length
`v^2 =p^2/((2l)^2)[F/m]`
`implies [m]=[(p^2F)/(4l^2v^2]] =([MLT^(-2)])/([L^2][T^(-2)])=[ML^(-1)T^(0)]`