Question

A stone hangs in air from one end of a wire which is stretched over a sonometer. The wire is in unison with a certain tuning fork when the bridges of the sonometer are 45 cm apart. Now the stone hangs immersed in water at 4°C and the distance between the bridges has to be altered by 9 cm to re–establish unision of the wire with the same fork. Calculate the density of the stone. 

Answer 1

Let V be the volume and ρ be the density of the stone. In air tension in wire 

F = Vρg . 

When hanged in water, then tension in the wire

F' = Vρg - Vρ_ωg

For two lengths L and L', we have