Question

Four fifth of a cylindrical block of wood floats in liquid is relative density of a the wood is 0.7 find the density of liquid

Answer 1

can you elaborate please

Answer 2

Let us assume that the weight of the wood submerged in liquid is w.  

It is given that 4/5th of the wood is submerged in the liquid.  

So the volume of liquid displaced = 4/5th of volume of wood.

From following equation, we can derive the volume of liquid displaced  

Volume = Weight/density

Volume of liquid displaced = 4W/5*d = 4W/5*0.7 = 8W/7

Let ‘d’ be the density of liquid.  

So weight of the liquid displaced = volume * density = 8Wd/7

Now from Archimede’s law, In the case of an object that floats, the amount of fluid displaced will be equal in weight to the displacing object.

Hence W = 8wd/7

So d = 7/8 = 0.87 gm/cc.

Hence density of liquid is 0.87 gm/cc