to ponder
means to, over a period of time, think about the consequences of two or more choices in a decision. If there is only one thing you are pondering, you are pondering whether or not to do that thing.
to mull over
is the same as ponder - but you can mull over collective nouns, meaning you are trying to decide which one of the group. "I mulled over the candy, and found a good piece."
to contemplate
means to think about the consequences of something carefully, thoroughly, and for a long time. Typically when you contemplate something, you are deciding whether or not to do it, not picking among an array of choices. It has a serious connotation, likely due to the common phrase contemplate suicide.
to cogitate
I don't hear this word a lot. According to Google, it can be used intransitively, so you don't have to be cogitating about anything in particular. The other words here generally require a "target" to make sense.
to deliberate [on]
means the same as contemplate. When I hear this word, I think of court proceedings or meetings ("the jury will deliberate... etc.").
to ruminate
I don't hear this in speech very much. In my opinion it's a "less serious" version of contemplate.
to dwell on
means to think about something over and over. It could be the consequences of a decision not yet made, a decision that just has been made, or it could be going over past events in your mind. Dwell on can have a negative connotation, possibly that what you are dwelling on is bothering you or haunting you.
So, I would answer like this:
("depth 10k worths" doesn't make sense to me, so the second is a guess)
I have been dwelling on my son (all day) since he left home for college.
I have been mulling over my depth 10k worths because I will have to pay it by next week but I don't have enough money. So I have to find a way.
I have been dwelling on my new school project. I don't know where to start.
The government deliberated how to stop protest on raising student fees.
Best Answer
In this context, there's no much difference I'd say. Nevertheless, this makes it food for thought. The difference between 'help' and 'support.'
Well, help is something that takes off your learning and you are not that active. On the other hand, support does require your active participation in doing things.
The best example I can think of is doing my homework. If Mike helps me do my homework, it may mean that he did it all! On the otehr hand, if Mike just supports me to perform the same task, he's helping me as and when needed. To make it even simpler, Mike will write down the table of 13 that I don't know at all. That's the help. If he supports me, he'd wait for the moment I get stuck! He'll then tell me the answer.
Take the help of Google, and you know Triskaidekaphobia. It's direct...not many efforts are needed. But when you have your software and you have Google's API to support, it at least requires you to build software on your own, and then take support of Google. Certainly not direct!
Psychologically, help is just a direct serve. Support could be mental as well. A person if boosting your moral when needed would be supporting you more. That's why we have moral support and NOT moral help. help is more obligatory. That's why probably we have helplessness that shows requirement of some sympathy or mercy.
But, let me repeat, in most of the cases, don't dig further! Let them go together without a big change in the meanings.