Question

As the bob is lowered gradually into water, how do the forces of upthrust and tension (in the string) change?

Answer

When the bob is entering the water, it displaces more and more water. The water thus exerts a larger and larger upthrust on the bob. By Newton’s 3^rd Law, the bob exerts a larger and larger “downthrust” on the water (and beaker). Since the density of water is about 1 g cm^-3, every 1 cm³ displacement of water means an additional upthrust of 1 gram times 9.81 ms^-2, which is reflected by a 1 gram increase in the weighing balance reading.

When the bob is fully submerged, lowering it further does not lead to any increase in upthrust, since the amount of water displaced is the same (even though the pressure around the bob keeps increasing. Why?). This is reflected by the constant weighing balance reading.

When the bob touched the bottom of the measuring cylinder, it begins to exert a downward contact force on the cylinder. (And the tension in the string starts to weaken). This is reflected by the increase in the weighing balance reading.

When the bob has fully landed, the string is slack so tension has dropped completely to zero. The weight of the bob is now fully supported by upthrust and contact force, which are both reflected in the weighing balance reading.

The graph above shows how the forces of tension, upthrust and the normal contact force (that the beaker exerts on the bob) vary as the bob was lowered. (Note that the reading on the weighing balance corresponded to the upthrust and normal contact force.)

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