How Much of the Wooden Block Emerges When Floating in Water Compared to Alcohol?

[dude123]

Homework Statement

A wooden block floats in alcohol with 3/8th of it's length above alcohol. If it is made to float in water , what fraction of it's length is above water? [Density of alcohol = 0.8 gm/cc]

Homework Equations

density = mass/Volume

The Attempt at a Solution

5/8 of the block is under the alcohol. So the volume of the displaced fluid is 5/8V where V is volume of the block. density = mass/volume so: 0.8g/cc = m/[(5/8)V] m = (5/8) V (0.8g/cc) Then I got the buoyant force -: F = (5/8) V (0.8g/cc) g . After this i create such equation for water with water's density and fraction of block is submerged but how can i relate them :?

 

[Carid]

Well the buoyant force will be the same (weight of block doesn't change) but the 5/8 figure will be some thing different, say K.

(5/8)*V*0.8 = K*V*1.0

so cancel out the V's and we get

K = (5/8)*0.8 = 0.5

 

[dude123]

ah yes , duh @ me :|
Thanks a lot Carid :)