- #1

icystrike

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## Homework Statement

An object made entirely from one material has a volume of 30m

^{3}. It floats in a liquid of density of 3g/cm

^{3}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/cm

^{3}If the final upthrust that will act on the object is expressed in the form of [tex] a × 10^{b} N [/tex] give the value of a and b. [Assume g = 10m/s

^{2}]

**The answer stated is 3 × 10**

^{3}I got a different solution, please kindly advice.

Thanks :)

## The Attempt at a Solution

Hyrdostatic force is : ρVg = 3 g/cm

^{3}× 1000 cm

^{3}/m

^{3}kg/g × 15m

^{3}× 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/30m

^{3}= 1500 kg/m

^{3}

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

F= ρVg = 1 g/cm

^{3}× 1000 cm

^{3}/m

^{3}kg/g × 30m

^{3}× 10 N/kg = 300'000N = 3 × 10

^{5}N

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