Question

a teacher demonstrates buoyancy, a property of water, by placing various objects in water. a student observes how some small objects, like a metal nail and a marble, sink when they are put in water. the student thinks about how huge cargo ships float on the surface of the water. what explains this phenomenon?
the forces of gravity pulling down on the nail (weight), is less than the buoyant force pushing upwards. this causes the nail to sink.
the force of gravity pulling down on the ship is less than the buoyant force pushing upwards. this causes the ship to float.
the force of gravity pulling down on the ship is greater than the buoyant force pushing upwards. this causes the ship to float.
the force of gravity pulling down on the nail (weight), is greater than the buoyant force pushing upwards. this causes the nail to sink.

Explanation:

To explain why huge cargo ships float, we use the principle of buoyancy (Archimedes' principle). A ship's hull is designed to displace a large volume of water. The buoyant force ($F_b$) equals the weight of the displaced water ($F_b =
ho_{water} V_{displaced} g$). For a ship, the total weight (gravity force, $F_g = m_{ship} g$) is balanced by the buoyant force when $F_b \geq F_g$. Even though the ship is massive, its hollow structure displaces enough water so that the buoyant force (upward) is at least equal to the gravitational force (downward), allowing it to float. Small objects like a metal nail have a density greater than water, so their weight exceeds the buoyant force from the small volume of water they displace, causing them to sink.

Answer:

The force of gravity (pulling down on the ship, its weight) is equal to or less than the buoyant force (pushing upward, from displaced water). The ship’s design (hollow, large volume displacement) means it displaces enough water so the buoyant force balances gravity, allowing it to float (unlike dense, small objects where weight > buoyant force, so they sink).