The frequency of a sonometer wire is `10 Hz`. When the weights producing the tension are completely immersed in water the frequency becomes `80 Hz` and on immersing the weights in a certain liquid the frequency becomes `60 Hz`. The specific gravity of the liquid is

Options

A. `1. 42`
B. `1.77`
C. `1.82`
D. `1.21`

Answer

B

Explanation

frequency ` f prop sqrt(mg)`
or `f prop sqrt(g)`
In water , `f_(w) = 0.8 f_(air)`
`:. (g')/(g) = (0.8)^(2) = 0.64`
or ` 1 - ( rho _(w))/(rho_(m)) = 0.64`
or `(rho _(w))/(rho_(m)) = 0.36` (i)
`- (rho _(L))/(rho_(m)) = 0.36`
or `(rho_(L))/(rho_(m)) = 0.64` (ii)
From eqs.(i) and (ii),
`(rho_(L))/(rho_(m)) = (0.64)/(0.36) = 1.77`