A sonometer wire is stretched by a hanging metal bob. Its fundamental frequency is `n_1`. When the bob is completely immersed in water, the frequency becomes `n_2` . The relative density of the metal is

Options

A. `(n^2)/(n_1^2-n_2^2)`
B. `(n_2^2)/(n_1^2-n_2^2)`
C. `(n_1)/(n_1-n_2)`
D. `(n_2)/(n_1-n_2)`

Answer

A

Explanation

`n^2 = (1)/(4l^2)(T_1)/(m)`
`T_1=(4l^2m)n_1^2`
`T_2 = (4l^2 m)n_2^2`
Relative density of material is
`=(T_1)/(T_1-T_2)=(n_1^2)/(n_1^2-n_2^2)`