You don't get two answers if you use a better model. In particular the model that you are using of a diode equals a battery is insufficient for this problem.
Batteries can both source and sink current. Batteries have finite internal resistance. Adding a perfect diode in series with the battery...
You can model a silicon diode as a 0.7V battery in series with a "perfect" diode. A little more care is required when modelling a germanium diode as a 0.3V battery and a "perfect" diode as germanium diodes leak a lot more than silicon under reverse bias. Leakage won't be an issue for this circuit.
Yes you can use just one hand for both. It is much better to use the right hand to give the direction of a magnetic field around a conductor which you can then visualise interacting with the field from the magnets. It is much better to just use the right hand for the vector cross product...
I tried the simpler problem of two bubbles of the same radius which makes the common surface a flat disc. My algebra got messy on that one too, so I did some approximating and ended with each bubble's radius increasing by approx 6%. Which means I'd be offering 1.06R as the distance between the...
Is there a fairly simple equation for the volume of the two bubbles once they have touched? There is a relationship for the three radii of a double bubble 1/Rcommon = 1/Rsmall - 1/Rlarge . Which can give another equation that relates the change in radius of the smaller bubble to the larger...
Your updated circuit in post #3 has a different value for one of the resistors compared to post #1.
How can current flow in your circuit? Is the 7V battery connected to one resistor or two?
Each of your components has two nodes. The resistors don't care which way around they are connected as they are symmetrical devices, is this the case with the two batteries? The voltmeter has two nodes too, does it care how it is connected?
I suspect the reason you are unsure of the answer is...
Since you want to be precise:
Is your circuit a loop or a line? You have described components connected in a line which would result in zero current in both resistors.
Where is the "point above the earth" as that is not a named node in your series circuit ? If this is a new node then this...
The directions of the forces associated with friction between a pair of surfaces always acts to reduce the relative motion between the two surfaces. To apply this to a situation where there is no slip imagine the motion that would take place if friction between the two surfaces was zero.
To expand on nasu's hint..
What other equations do you know that might be relevant? While it is great if you instantly know the correct equation to use, when unsure a list of equations that might be useful along with a table of knowns and unknowns for each equation can often illuminate how to...