When a ship floats on water, it displaces a certain volume of water equal to its own weight. This principle is known as Archimedes` principle. Option 1, which states that a ship displaces no water, is incorrect. Option 3, which suggests that the mass of water displaced is lesser than the mass of the ship, is also incorrect. The correct answer is Option 2, which states that the mass of water displaced is equal to the mass of the ship.

Archimedes` principle explains that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. In the case of a ship floating on water, the buoyant force acting on the ship is equal to the weight of the water displaced by the ship. This allows the ship to stay afloat. If the ship were to displace less water than its own weight (Option 3), it would sink. Similarly, if the ship were to displace more water than its own weight (Option 4), it would float higher in the water. Therefore, Option 2 accurately describes the relationship between the mass of water displaced and the mass of the ship when it floats.