A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are L cm apart when the wire is in unison with a tuning fork of frequency N . When the stone is completely immersed in water, the length between the bridges is l cm for re-establishing unison, the specific gravity of the material of the stone is

Options

A. `(L^(2))/(L^(2)+l^(2))`
B. `(L^(2)-l^(2))/(L^(2))`
C. `(L^(2))/(L^(2)-l^(2))`
D. `(L^(2)+l^(2))/(L^(2))`

Answer

C

Explanation

`f=(1)/(2l)sqrt((T)/(mu))`
When the stone is completely immersed in water, length changes, but frequency remains constant
`lpropsqrt(T)implies(L)/(l)=sqrt((T_("air"))/(T_("water")))=sqrt((V_(rhog))/(V(rho-1)g))`
`implies (L)/(l)=sqrt((rho)/(rho-1))impliesrho=(L^(2))/(L^(2)-l^(2))`.