A block of wood is floating in water such that 1/ 3 rd of it is submerged in water when the same block is floated in alcohol, 1/2 of it's volume is submerged. Now a mixture of water and alcohol i

Question

A block of wood is floating in water such that 1/ 3 rd of it is submerged in water when the same block is floated in alcohol, 1/2 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 ?

TestHub · Accepted Answer

mg = ρ w ​ 3 v ​ g = ρ A ​ 2 v ​ g ​ ρ mixture ​ = 2 v 0 ​ ρ w ​ v 0 ​ + ρ A ​ v 0 ​ ​ = 2 ρ w ​ + ρ A ​ ​ ​ mg = [ 2 ρ w ​ + ρ A ​ ​ ] × [ n v ​ ] g … ( ii ) ​ From equation (i) & (ii) ρ w ​ 3 v ​ g = 2 n vg ​ [ ρ w ​ + 3 2 ρ w ​ ​ ] ; 3 1 ​ = 2 n 1 ​ [ 3 5 ​ ] ⇒ n = 2 5 ​

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