A block of wood is floating in water such that `1//2` of it is submerged in water when the same block is floated in alcohol, `1//3^(rd)` of it's volume is submerged Now a mixture of water and alcohol is made taking equal volume of both and block is floated in it. What is the % of it's volume that is now submerged?

Explanation

0040
`mg=rho_(1)xx0.5V_(0)g impliesrho_(2)=(2m)/(V_(0))`
`mg=rhoxx(V_(0))/(3)gimpliesrho_(2)=(3m)/(V_(0))`
`rho=(rho_(1)V+rho_(2)V)/(2V)=(rho_(1)+rho_(2))/(2)`
`mg=rhoVg=((rho_(1)+rho_(2))Vg)/(2)impliesm=(1)/(2)((2m)/(V_(0))+(3m)/(V_(0)))V`
`m=(5mV)/(2V_(0))`
`V=0.4V_(0)implies40%`