Question

A wooden block floats in alcohol with 3/8 of its length above alcohol. If it is made to float in water, what fraction of its length is above water? Density of alcohol is 0.80 g cm^-3.

Answer 1

Let length of wooden block = x

∴ Length of the block above alcohol = `3/8`x

Length of the block below alcohol 

`= "x" - 3/8"x" = ("8x" - "3x")/8 = "5x"/8`

Density of water = `rho_"w" = 1 "gcm"^-3`

Density of alcohol = `rho_"alcohol" = 0.80 "gcm"^-3`

By the law of floatation:

`"h"_"block" xx rho_"block" = "h"_"alcohol" xx rho_"alcohol"`

`"x" xx rho_"block" = "5x"/8 xx 0.80`

`rho_"block" = 5/8 xx 0.80`

`rho_"block" = 0.5` gcm^-3

When the block is floating in water:

By law of floatation:

`"h"_"block" xx rho_"block" = "h"_"water" xx rho_"w"`

`"x" xx 0.5 = "h"_"water" xx 1`

`"h"_"water" = 0.5  "x"  "or"  1/2 "x"`

So, length of block above water = `"x" - 1/2"x" = "x"/2`

Fraction of the block above the water = `"x"/2 xx 1/"x" = 1/2` part

`=> 1/2 "th"` part of wooden block is above the water.