Figure shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.
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Answer

`[5.76 xx 10^(3) kg//m^(3)]`

Explanation

Initially we use frequency of force,
`n_(f) = (10)/(2l)sqrt((mg)/(mu))`
after block is dipped in water we use
`n_(f) = (11)/(2l) sqrt((mg(1 - rho_(omega)//rho_(b)))/mu)`
from (1) & (2) we use
`10 = 11sqrt(1 - rho_(omega)//rho_(b))`
`100 rho_(b) = 121 rho_(b) - 121 rho_(omega)`
`rho_(b) = (121rho_(omega))/(2I) = 5.76 xx 10^(3) kg//m^(3)`