Question

A ship of total mass 1200000 kg floats in fresh water. What mass of cargo should be unloaded so that the ship does not sink any further? (Density of fresh water = 1000 kg/m³)

(A) 12000 kg
(B) 24000 kg
(C) 36000 kg
(D) 48000 kg

Answer 1

To make the ship float without sinking any further, 1200000 kg of cargo should be unloaded.

Step-by-step explanation:

In order for the ship to float, the buoyant force acting on the ship must equal the weight of the ship. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.

The weight of the ship is given as 1200000 kg. To find the weight of the fluid displaced, we need to find the volume of the ship and multiply it by the density of fresh water.

Let's calculate the volume of the ship:

Volume = mass/density = 1200000 kg / density of fresh water = 1200000 kg / 1000 kg/m³ = 1200 m³

Now, let's calculate the weight of the fluid displaced:

Weight of fluid displaced = volume x density of fresh water = 1200 m³ x 1000 kg/m³ = 1200000 kg

To make the ship float without sinking any further, the weight of the cargo unloaded must be equal to the weight of the fluid displaced. Therefore, 1200000 kg of cargo should be unloaded.