A block of wood floats in a liquid of density 0.8g/cm sq. with one fourth of its volume submerged. In oil the block floats with 60% of its volume submerged. Find the density of (a) wood? (b) oil?

Let the volume of the block of wood be ##V cm^3## and its density be ##d_w gcm^-3##

So the weight of the block ##=Vd_w g## dyne, where g is the due to gravity ##=980cms^-2##

The block floats in liquid of density ##0.8gcm^-3## with ##1/4 th## of its volume submerged.So the upward buoyant force acting on the block is the weight of displaced liquid##=1/4Vxx0.8xxg## dyne.

Hence by cindition of floatation

##Vxxd_wxxg=1/4xxVxx0.8xxg##

##=>d_w=0.2gcm^"-3"##,

Now let the density of oil be ##d_o gcm^"-3"##

The block floats in oil with 60% of its volume submerged.So the buoyant force balancing the weight of the block is the weight of displaced oil = ##60%xxVxxd_o xxg## dyne

Now applying the condition of floatation we get

##60%xxVxxd_o xxg=Vxxd_wxxg##

##=>60/100xxcancelVxxd_o xxcancelg=cancelVxx0.2xxcancelg##

##=>d_o=0.2xx10/6=1/3=0.33gcm^-3##