A beaker resting on a scale contains a fluid. If an object is submerged in the fluid, by how much does the reading of the scale increase?
The correct answer and explanation is:
Correct Answer:
The reading of the scale increases by an amount equal to the weight of the object that is submerged in the fluid.
Explanation (300 words):
When an object is submerged in a fluid contained within a beaker resting on a scale, the scale measures not only the weight of the fluid and the beaker but also the effect of the submerged object. The key principle at play here is Newton’s third law of motion, which states that every action has an equal and opposite reaction, along with Archimedes’ principle, which explains buoyant force.
As the object is placed into the fluid, it displaces a certain volume of that fluid, which results in an upward buoyant force acting on the object. This buoyant force is equal to the weight of the displaced fluid. However, the object also exerts an equal downward force on the fluid. That downward force is then transferred to the beaker and ultimately to the scale. This causes the scale reading to increase.
Importantly, regardless of the buoyant force acting on the object, the scale’s reading increases by the total weight of the object if the object is fully supported by the fluid. Even though part of the object’s weight is balanced by buoyancy, the fluid and beaker must support the full object through pressure. This is why the weight of the object is effectively transmitted to the scale.
If the object is held and not allowed to rest completely in the fluid, only the weight of the displaced fluid (equal to the buoyant force) is added to the scale reading. But if the object is fully submerged and not held, the entire weight of the object is added.
Therefore, the increase in the scale reading equals the weight of the object when it is fully submerged and supported only by the fluid inside the beaker.