Question

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?

Answer 1

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 acceleration 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`