I'm currently an undergraduate sophomore at Rutgers double majoring in Physics and Mechanical Engineering. I've recently made the decision that I want to go for a master's degree in physics and then potentially a PhD. However, I'm doing research in mechanical engineering right now and I don't think I'll have a strong enough physics background by next Fall to undertake physics research. My GPA is very high and I'm confident I can do well on the GRE, but the research aspect is concerning. My goal is to get into a top 10 school for Physics. Is that achievable without having done research? I'm planning on continuing doing research in mechanical engineering related to some branch of physics (maybe thermal) and do research in physics my senior year, but I feel like I'm behind competitors. I also won't be able to take many graduate classes in physics (only 1-2). Will this hinder my chances of being able to attend a school like Princeton or Berkeley or MIT?