A 4900-newton stone floats after displacing 9800 newtons of water.

A rock, a pool, and a little buoyancy magic — that’s the neat takeaway from this little physics puzzle you’ll see in LMHS NJROTC contexts. Here’s the scenario in plain terms: a stone weighs 4900 newtons in air. When it’s fully submerged in water, it displaces 9800 newtons worth of water. The multiple-choice options ask what happens to the stone, and the correct answer is: it floats.

Let me explain how that works, without getting lost in jargon. It all comes down to Archimedes’ principle. In simple terms: the water pushes back on a submerged object with a buoyant force that equals the weight of the water that’s been displaced by the object. If that upward push is bigger than the stone’s weight, the stone won’t stay under water. It will start to rise until the two forces balance out.

So, in numbers here: when the stone is fully under water, it would have a buoyant force of 9800 newtons (because that’s the weight of the water it’s displacing). The stone’s own weight is 4900 newtons. Since 9800 is greater than 4900, there’s a net upward force. Translation: the stone tends to rise.

When it rises, the amount of water it displaces decreases, until the buoyant force exactly matches the stone’s weight. That’s the equilibrium where it stops rising. In this particular setup, you can think of it this way: the maximum buoyant force you could get if the stone were completely submerged is 9800 N. To balance a weight of 4900 N, the stone only needs half of its volume submerged. In other words, about 50% of the stone stays underwater and the rest sticks out above the surface. So the stone floats, not sinks.

A quick mental model helps a lot here. If you imagine the stone as having a certain density and volume, the fraction of the stone that sits below the water line when it’s floating is determined by the ratio of its weight to the buoyant force it would experience if it were fully under water. Because 4900 N is half of 9800 N, roughly half of the stone must be underwater to balance the forces. It’s a nice, tidy example of why ships and boats float despite carrying heavy cargo: they push a lot of water aside, generating a buoyant push that keeps them afloat.

This particular problem also sheds light on a broader idea: density isn’t the only thing that decides sinking versus floating. It’s the relationship between the weight of the object and the weight of the water it displaces. A rock typically has a density greater than water and sinks. But here, the numbers don’t force sinking — they tip the balance the other way. If a thing’s volume is large enough relative to its weight, it can displace a lot of water and still ride the surface. That’s exactly what’s happening to our stone.

For you, as you’re studying topics that come up in naval-tinged academic settings, this is a handy reminder:

• Archimedes’ principle is the star player: buoyant force equals the weight of displaced water.

• If buoyant force exceeds the object’s weight, the object rises and eventually floats.

• The fraction submerged when floating is roughly the weight divided by the buoyant force you’d get if the object were fully submerged. In this case, 4900/9800 ≈ 0.5, so about half the stone is underwater.

A few digressions that connect this to real life (and to the kind of thinking you’ll use in the NJROTC sphere):

• Boats aren’t magic; they’re big, carefully shaped masses that push a lot of water aside. The hull geometry, the air inside compartments, and even ballast are all about managing buoyant forces.

• Life jackets rely on this same principle in a practical way: they’re designed to displace enough water to keep a person’s head above the surface, even when the wearer is heavy.

• Submarines do the opposite they’re designed to control buoyancy with ballast tanks, letting them sink or rise by changing how much water sits in those tanks.

If you’re ever in a pool or near a shoreline, you can see this principle in action with a simple thought experiment. A light, bulky object will float high with most of its volume above water; a denser, heavier object will sink. The twist here is that, with the numbers given (4900 N weight, 9800 N buoyant potential), the stone behaves in a way you might not expect from a typical rock: it settles into a floating state with half of its volume submerged. That contrast—that the same material can act so differently simply because of the surrounding water’s push—is a great example of why buoyancy is a foundational concept in physics and in naval science alike.

A practical takeaway you can carry into lessons and everyday observations: always compare the weight of the object to the buoyant force it could experience if fully submerged. If the buoyant force is greater, the object will rise and eventually float. If the weight is greater, it sinks. And if they’re precisely balanced, you’ll have a neutrally buoyant situation, where the object neither rises nor sinks. In our stone’s case, the numbers point to floatation with roughly half its volume underwater.

One last thought before you close this chapter of the water-and-weight puzzle: the idea isn’t about magic; it’s about how pressure, density, and displacement interact. It helps explain not only everyday scenes like a rock in a pond but also the design choices behind ships, submarines, and even paddling gear. The next time you see a boat gliding across the surface, you’re watching Archimedes in motion — an ancient principle still guiding modern watercraft, what we might call the quiet backbone of afloat-friendly engineering.

In short: the stone floats. The buoyant force from the displaced water is bigger than the stone’s weight, so the stone meets the water’s push halfway and calmly stays afloat. That’s buoyancy in action — a simple, elegant balance that shows up in all kinds of maritime and water-world scenarios.