Question

A body floats in water with 40% of its volume out side the
water. When the body floats in oil, 60% of its volume remains
outside oil. What is the relative density of oil?​

Answer 1

Answer:

1500 kg/m^3 or 1.5 g/cm^3

Explanation: As per law of floatation

Mg = Weight of fluid displaced by body

Let V be total volume of body

D be the density of body

v be the volume of fluid displaced

d be the density of fluid

In case of water,

Mg = Weight of fluid displaced

V x D x g = v x d x g (water)

⇒ V x D x g = 60/100 x 1000 x 10

In case of oil

Mg = Weight of fluid displaced

V x D x g = v x d x g (oil)

⇒V x D x g = 40/100V x D x 100

Now, from the two equations

60/100 x V x 1000 x 10 = 40/100 x V x d x 10

d = 6000/4

d = 1500 kg/m^3

Answer 2

Answer:

Let :

V = volume of body

ρ = density of liquid

ρ₀ = density of water.

= > Weight of body = Upthurst .

Weight of body = ( 100 - 40 ) V ρ₀  g / 100

= > ( 100 - 60 ) V ρ g / 100

Now relative density :

R.D. = ρ / ρ₀

= > R.D. = 0.6 / 0.4

= > R.D. = 1.5

Therefore , relative density of water is 1.5 .