B

Step 1: Understand the setup
We have an open beaker being dipped into water in two orientations: one with the bottom up (beaker 1) and another with the bottom down (beaker 2). The depth to which the beaker is submerged is the same in both scenarios.

Step 2: Analyze the scenarios
When the beaker is positioned with the bottom up, the water enters the beaker and starts to exert a buoyant force inside it. In this case, as the beaker is depressed, the air inside cannot escape initially, requiring additional work to push against the buoyancy caused by the air pressure and eventually leading to water displacement.
In contrast, when the beaker is positioned with the bottom down, the air inside can escape more easily when the beaker is pressed into the water, easing the pressure difference.

Step 3: Calculate work done
The work done to dip the beaker depends on the pressure and the buoyant forces acting on it. The upward buoyant force when the beaker is upside down (beaker 2) is less compared to what the beaker experiences when it's right side up (beaker 1) because less air volume needs to be displaced for the same depth of water.

Step 4: Conclusion
Since the beaker oriented with the bottom up (beaker 1) has to overcome a greater buoyant force due to both water and trapped air, it will require more work to submerge it compared to the bottom down configuration (beaker 2). Thus, more work must be exerted in the case of the beaker oriented bottom up.

Therefore, the correct answer is B.