A stone in hung in air from a wire which is stretched over a sonometer . The bridges of the sonometer are `40 cm` apart when the wire is in unison with a tuning fork of frequency `256 Hz`. When the stone is completely immersed in water , the length between the bridges is `22 cm` for re - establishing unison . The specific gravity of the material of the stone is

Options

A. `((40)^(2))/((40)^(2) + (22)^(2))`
B. `((40)^(2))/((40)^(2) - (22)^(2))`
C. `256 xx (22)/(40)`
D. `256 xx (40)/(22)`

Answer

B

Explanation

`f = (1)/(2 xx 40) sqrt((mg)/(mu)) = 256 …(1)`
`f = (1)/(2 xx 22) sqrt((mg - f_(b))/(mu)) = 256 …(2)`
`(mg - f_(b))/(mg) = ((22)/(40))^(2)`
`(v(1)g)/(vsigmag) = (40^(2) - 22^(2))/(40^(2))`
`sigma = (40^(2))/(40^(2) - 22^(2))`