The frequency of a sonometer wire is f . When the weight producting the tensions are completely. Immersed in water the frequency becomes `f//2` and on immersing the weight in acertain liquid the fequency becomes `f//3`. The specific gravity of the liquid is

Options

A. `4//3`
B. `16//9`
C. `15//12`
D. `32//27`

Answer

D

Explanation

` f=(1)/(2l)sqrt((W)/(mu))" "....(1)`
Now weight is immeresed in water. `(f)/(2)=(1)/(2l)sqrt((W-B)/(mu))" "....(2)`
From (1) and (2) `(1)/(2)xx(1)/(2l)sqrt((W)/(mu))=(1)/(2l)sqrt((W-B)/(mu))" "impliesB=(3)/(4)W`
`Vrho_(w)g=(3)/(4)Vrhogimplies rho_(w)=(3)/(4)rho" "...(3)`
Now weight is immeresed in liquid `(f)/(3)=(1)/(2l)sqrt((W-B)/(mu))" "....(4)`
From (1) and (4) `B=(8)/(9)Wimplies " "Vrho_(l)g=(8)/(9)Vrhogimpliesrho_(l)=(8)/(9)rho" "....(5)`
From (3) and (5) `rho_(l)=(32)/(27)rho_(w)`