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

5.8x10^3kg/m^2`

Explanation

Let `rhorarr` density of the block
`weight= rhoVg`
Where V=volume of block.
The same tunning fork resonates with string in the two cases.
`f_10=10/(2L) sqrt(T/m)`
`=10/(2L) sqrt(rhoVg)/m`
`(mrarr `mass per unit length of string)
When the block is immersed in water
`f_11=11/(2L) sqrt((T-rho_wVg)/m)`
`=11/(2L) sqrt((rho-rho_w)Vg)/m`
As the for of tunning fork is same
`f_10=f_11=10/(2L) sqrt((rhoVg)/m)`
`=11/(2L)sqrt(((rho-rho_w)Vg)/m)`
`rarr 10/(2L)sqrt((rho-rho_w)/m)=(rho-1)/rho= 100/121`
`(because rhow=1(gm)/cc)`
`rarr 100 rho=121rho-121`
`rarr rho=121/21`
`=5.8(gm)/cc`
`=5.8(gm)/cc`
`=5.8x10^3(kg)/m^3`