Answer :
The mass of the box is 2500 kg.
To solve this problem, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The buoyant force (B) can be calculated as:
B = ρ_fluid * V_box * g
where:
ρ_fluid is the density of the fluid (water) in kg/m^3,
V_box is the volume of the box in m^3, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
The weight of the box (W_box) can be calculated as:
W_box = m_box * g
where m_box is the mass of the box.
Since the box is just barely able to be lifted to the surface, the buoyant force (B) is equal to the weight of the box (W_box).
Equating the two expressions for weight and buoyant force:
ρ_fluid * V_box * g = m_box * g
We can cancel out the acceleration due to gravity (g) from both sides:
ρ_fluid * V_box = m_box
Now, let's plug in the given values:
Density of water (ρ_fluid) ≈ 1000 kg/m^3 (approximately)
Volume of the box (V_box) = 2.5 m^3
m_box = ρ_fluid * V_box
m_box = 1000 kg/m^3 * 2.5 m^3
m_box = 2500 kg
So, the mass of the box is 2500 kg.
Learn more about buoyant force from the given link
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