Answer
The water level falls.
Work Step by Step
Archimedes' Principle
An object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of fluid displaced by the object.
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With the pebble in its mouth, the fish is not accelerating up or down, so the buoyant force equals the weight of the fish+pebble. The volume of water displaced has the weight of the fish + the weight of the pebble.
When the pebble is dropped, the fish is still in vertical equilibrium, and displaces water equal to its weight (without the pebble). The pebble is accelerating down, its weight is greater than the buoyant force acting on it (it displaces a volume of water equal to its volume, not its weight). Because the density of the pebble is greater than that of the water, the volume of water displaced is LESS than it was before, when the pebble was in the fish's mouth.
Less water is displaced than before and hence, the level falls.
