I applied for a PhD position, with my own research proposal, at a university and received an offer already. However, as I cannot fund myself, I have to wait for the scholarship decision which will be announced at the end of April.
In the meantime, the university is advertising an industrially funded PhD project whose deadline is end of March. My background matches the requirements for the project, which is quite interesting to me, too. I wonder if I should apply for this project as well. If I am accepted and receive a scholarship from the first offer, I have to choose one of them.
Update: I'm asking this question as I'm worried that making two applications to two supervisors from the same research group may impact the outcome of both applications, i.e. whether I receive a scholarship for the first application and/or be accepted into the 2nd project. I am worried because I believe both supervisors would not be very happy if they knew about me applying to both positions.