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?

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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?

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Answer 1 · 2016-11-03T11:33:27

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

$60%xxVxxd_o xxg=Vxxd_wxxg$

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

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

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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

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