A solid object floats on ethyl alcohol, with 68.2%of the object’s volume submerged .Find the density of the object. Take density of alcohol =806 kg/m

math ..

Oh ,,I am sorry , I mean science

mg=F(buoyant),

ρ₁Vg=ρ₂0.64Vg,
ρ₁=0.64ρ₂=0.64•806=515.84 kg/m³.

To find the density of the object, we need to use the principle of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid.

The buoyant force is given by the formula:

Buoyant force = (density of fluid) * (volume of fluid displaced) * (acceleration due to gravity)

In this case, the fluid is ethyl alcohol, and we know its density, which is 806 kg/m³.

The volume of fluid displaced by the object is given as 68.2% of the total volume of the object.

Let's assume the volume of the solid object is V, and the volume submerged is V_submerged. From the information given, we know that V_submerged = 0.682 * V.

Now we can calculate the density of the object using the buoyant force equation.

Buoyant force = (density of fluid) * (volume of fluid displaced) * (acceleration due to gravity)

Since the object is floating, the buoyant force equals the weight of the object.

Weight of the object = (density of object) * (volume of object) * (acceleration due to gravity)

Setting these two forces equal to each other, we can solve for the density of the object.

(density of object) * (volume of object) * (acceleration due to gravity) = (density of fluid) * (volume of fluid displaced) * (acceleration due to gravity)

Canceling the acceleration due to gravity, we get:

(density of object) * (volume of object) = (density of fluid) * (volume of fluid displaced)

Substituting the known values, we get:

(density of object) * V = (806 kg/m³) * (0.682 * V)

Simplifying the equation, we find:

density of object = (806 kg/m³) * (0.682)

density of object ≈ 549.692 kg/m³

Therefore, the density of the object is approximately 549.692 kg/m³.