A ship has an area of cross section at the water line 2000m square

(a). By what depth does the ship sink in fresh water when it loads a cargo of 4000 tonnes
(b). If the ship plus the cargo has a displacement turnnage of 123000 tonnes, by what amount will the ship rise in the water it sails from fresh water into sea water.
Density of sea water =1000kg

Pls school are u going to

To find the depth by which the ship sinks in fresh water when it loads a cargo of 4000 tonnes, we can use Archimedes' principle.

(a) By Archimedes' principle, the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force (F_b) can be calculated using the formula:
F_b = ρ * g * V
where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid displaced.

In this case, the fluid is fresh water, so the density (ρ) is 1000 kg/m^3. The volume of water displaced can be calculated from the area of cross-section of the ship (A) and the depth of submersion (h):
V = A * h

The weight of the cargo (W) can be calculated using the formula:
W = m * g
where m is the mass of the cargo (4000 tonnes or 4000000 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Equating the buoyant force to the weight of the cargo:
F_b = W

ρ * g * A * h = m * g
h = (m * g) / (ρ * A)

Substituting the values, we get:
h = (4000000 kg * 9.8 m/s^2) / (1000 kg/m^3 * 2000 m^2)

Calculating this, the depth by which the ship sinks in fresh water when it loads a cargo of 4000 tonnes is approximately 19.6 meters.

(b) To calculate the amount by which the ship will rise in the water when it sails from fresh water into sea water, we use the same principle.

The buoyant force (F_b) experienced by the ship can be calculated using the same formula:
F_b = ρ * g * V

However, in this case, the fluid is sea water, so the density (ρ) is 1000 kg/m^3. The volume of sea water displaced can be calculated from the ship's displacement tonnage (DT). Displacement tonnage is a measure of the weight of the water displaced by the ship, and it is equivalent to the mass of the ship and its contents.

The volume of sea water displaced (V_sw) is given by:
V_sw = DT / ρ_sw
where ρ_sw is the density of sea water (1000 kg/m^3).

The ship will rise in the water by an amount equal to the difference in volumes between the fresh water and sea water:
ΔV = V_sw - V_fw
where V_fw is the volume of fresh water displaced.

Using the volume formula V = A * h, we can rewrite the equation as:
ΔV = A * (h_sw - h_fw)
where h_sw is the depth of submersion in sea water.

From equation (a), we know that
h_fw = (m * g) / (ρ * A)

Substituting the values and rearranging the equation, we get:
ΔV = A * [(DT / ρ_sw) - (m * g) / (ρ * A)]

Simplifying further, we get:
ΔV = DT / ρ_sw - m * g / ρ

Substituting the given values, we get:
ΔV = 123000 tonnes / (1000 kg/m^3) - 4000000 kg * 9.8 m/s^2 / (1000 kg/m^3)

Calculating this, the ship will rise in the water by approximately 123.2 cubic meters when it sails from fresh water to sea water.