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?

1 Answer
P dilip_k
Nov 3, 2016

Let the volume of the block of wood be V cm^3Vcm3 and its density be d_w gcm^-3dwgcm−3

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

The block floats in liquid of density 0.8gcm^-30.8gcm−3 with 1/4 th14th of its volume submerged.So the upward buoyant force acting on the block is the weight of displaced liquid=1/4Vxx0.8xxg=14V×0.8×g dyne.

Hence by cindition of floatation

Vxxd_wxxg=1/4xxVxx0.8xxgV×dw×g=14×V×0.8×g

=>d_w=0.2gcm^"-3"⇒dw=0.2gcm-3,

Now let the density of oil be d_o gcm^"-3"dogcm-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 xxg60%×V×do×g dyne

Now applying the condition of floatation we get

60%xxVxxd_o xxg=Vxxd_wxxg60%×V×do×g=V×dw×g

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

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

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