A bucket of water is hung from a spring balance. A piece of iron is suspended in the water without touching the sides or the bottom of the bucket, using a separate support from above. How will the reading of the spring balance holding the bucket change?

Introduction / Context:
This question is a classic application of Archimedes' principle and Newton's third law. It explores how the apparent weight of a system changes when an additional object is immersed in a fluid without being directly supported by that system. Understanding how upthrust, reaction forces and weight interact in such setups is important for basic mechanics and hydrostatics, and this type of problem appears often in entrance and competitive exams.

Given Data / Assumptions:

• A bucket of water is hanging from a spring balance, so the balance measures the total weight of the bucket plus water.
• A piece of iron is suspended in the water from an external support above, not touching the sides or bottom of the bucket.
• The iron is fully or partly immersed, so it experiences upthrust from the water.
• The bucket, water and spring balance form one system; the iron and its support form another system.

Concept / Approach:
When the iron piece is immersed, it experiences an upward buoyant force equal to the weight of the water displaced. According to Newton's third law, the water experiences an equal and opposite downward force exerted by the iron. This extra downward force is transmitted to the bucket and then to the spring balance. As a result, even though the iron is not physically resting on the bucket, its presence in the water effectively increases the total downward force on the spring balance by exactly the buoyant force. Therefore, the reading on the balance increases.

Step-by-Step Solution:
Step 1: Initially, the spring balance reads the weight of the bucket plus water.Step 2: When the iron piece is immersed, it experiences upthrust equal to the weight of displaced water.Step 3: The iron pushes the water downward with a force equal to this upthrust (action–reaction pair).Step 4: This additional downward force is transmitted to the bucket and then to the spring balance.Step 5: Hence, the effective weight of the bucket–water system as seen by the balance increases by the buoyant force.Step 6: Therefore, the balancing reading must increase when the iron is immersed.

Verification / Alternative check:
Consider extreme cases. If instead of being hung from an external support, the iron were resting on the bottom of the bucket, the entire weight of the iron would be added to the reading. When it is hung separately and just immersed, at least the buoyant part of its weight still acts on the water and thus on the bucket. So the reading cannot stay the same or decrease; it must rise relative to the original state, although not by the full weight of the iron, only by the upthrust value.

Why Other Options Are Wrong:
The reading cannot decrease, because no upward force is being removed from the bucket; an extra downward force is being added. The reading does not remain unchanged, because the buoyant force introduces a new downward interaction. The suggestion that the reading varies with depth alone is misleading: once fully immersed, the upthrust depends on the volume of the displaced water, which is fixed for a given object, not on depth (assuming uniform density of water and ignoring compressibility). Thus, only the "will increase" option is correct.

Common Pitfalls:
Many students think that because the iron is supported from above, the bucket is unaffected. They forget that fluids transmit forces and that upthrust on the iron is accompanied by a reaction on the water. Another common mistake is to assume that buoyant force depends on depth, which is not true for incompressible fluids. Always remember: buoyant force equals the weight of displaced fluid, and any such interaction will influence the reading on a supporting balance.

Final Answer:
The reading of the spring balance will increase when the iron piece is immersed in the water.