Therefore, a = 3 and b = 5.Hydrostatic Force Homework: Find a & b

[icystrike]

Homework Statement

An object made entirely from one material has a volume of 30m³. It floats in a liquid of density of 3g/cm³ with only half its mass below the liquid's surface. The object is then placed in another liquid of same volume but with a density of 1g/cm³ If the final upthrust that will act on the object is expressed in the form of $$a × 10^{b} N$$ give the value of a and b. [Assume g = 10m/s²]

The answer stated is 3 × 10³

I got a different solution, please kindly advice.

Thanks :)

The Attempt at a Solution

Hyrdostatic force is : ρVg = 3 g/cm³ × 1000 cm³/m³ kg/g × 15m³ × 10 N/kg = 450'000 N

Since hydrostatic force = gravitational force,

The mass of the object will be : m = 45000N × 0.1 kg/N = 4500kg
The density of the object will be: ρ_object = 4500kg/30m³ = 1500 kg/m³

Since it is denser than the second liquid, the hydrostatic force experienced in the second liquid will be as follow:

F= ρVg = 1 g/cm³ × 1000 cm³/m³ kg/g × 30m³ × 10 N/kg = 300'000N = 3 × 10⁵ N

 

[TSny]

Your answer of 3 ×10⁵ N looks correct to me.