Okay, I'm afraid this is going to be a long reply...
graphene said:
Though they call it 'Engineering Physics', it is predominantly physics.
Yes, I have heard good things about this program. But it is a 4 year BTech program like all others in the IITs. I seriously doubt your claim that "it is predominantly physics". A full fledged engineering undergrad takes 4 years and an integrated MSc (which I consider equivalent in India to a full fledged physics undergrad) takes 5 years. As an IIT student, I'm sure you know well enough how packed things are in the program..and will appreciate that it is impossible to do two things in the space originally designated for courses of one major. (But I'm sure it helps psychologically, because we all know that its mostly nonacademic reasons which propel people into BTech programs. I too thought hard about this program, so I know

)
There are a lot of folks who go to grad school in engineering after an undergrad in physics (or even math) in the US and other countries. In India, this is made difficult because of a host of prerequisites in entrance exams. But it is possible to surmount those hurdles. IMHO, if you really want to "study" (different from "do"!) physics
and engineering
in India, the best way is to either do a dual major (IITs do not allow this, a minor is allowed at IITM and perhaps some others) or study engineering (the program is more competitive and you'll have to work much harder to study physics on the side, but the exposure is worth it). But if you hate engineering
already, and are sure of your interests in physics, then get into a physics program.
There were talks about doing a B.Tech (in engg.) & then trying to shift over to physics. But if you are interested in physics, and if you feel you have the aptitude for a research career in physics, go for one of these programs that I've mentioned rather than doing engg.
The OP seems to be constrained to study engineering. That being said, there is absolutely no problem in "switching" over to physics. It takes some effort, some extra preparation, but then what doesn't? If research in physics is what he wants to do eventually, it will be well his worth to put in that effort.
After a B.Tech in mech. engg / aerospace engg., physics would be totally different. Elec engg. is the closest to physics, but that's still quite far away.
Often comments are made on this forum about closeness of an engineering discipline to physics. While this is perhaps bothering you, please understand that every engineering discipline is strongly rooted in physics and mathematics, subjects you can never do without. Mechanical and aerospace engineering folks often get into physics programs, specializing in astronomy, astrophysics, fluid dynamics, thermodynamics/statistical mechanics, dynamical systems, chaos, to cite a few examples (with fluid dynamics being the area most of them can easily get into). EEs get into semiconductor physics, device physics, lasers, coherent optics, electromagnetics, quantum computing, etc. Oh and yes, I do know MEs and EEs who are 'full blown' theoretical physicists too.
Electrical engineering is indeed a LOT of physics, and I don't know what your metrics are when you say that it's "still quite far away". If your definition of physics is limited to familiarity with quantum mechanics, field theory, relativity and some of the more terse theoretical areas, then I don't see why closeness should be a consideration at all :-)
The dividing line at least between experimental physics, a lot of theory (cond-mat, amo, optics, lasers, ...) and engineering is very thin now..just look at the kind of research labs are engaged in. Some fringe areas of theoretical physics, such as superstring theory, high energy particle physics theory, and cosmology are still quite far removed from engineering, but usually one is not sure of his or her interests in 'fringe' areas until one has gained enough mathematical maturity and some research experience to be able to make a decision.
Now a bit about theoretical physics:- very few programs at the undergrad level (BSc) in India will prepare you well for the
meat of theoretical physics -- quantum mechanics, classical mechanics,
mathematical methods, electromagnetic theory, statistical mechanics. Yes, the 2 year MSc courses and the 5 year MSc courses at the IITs and other places listed by graphene, are of course great, if you can get to do those. But if you can't, then ironically even the physics undergrad won't prepare you well for grad school and research in theoretical physics!
In
summary, if you simply
cannot go to a school graphene suggested to study physics in your undergrad (BSc or MSc Int) for whatever reason (let's not get into that), then go ahead and join a good challenging engineering undergrad program, take lots of theoretical physics courses, read lots of things, and do lots of experiments. Have fun, and prepare for the entrance exams to TIFR, HRI (JEST) and also take the Physics GRE. Sustaining interest in physics is a key. If you can do that throughout the 3 or 4 years of your undergrad (whatever be the area) and you feel motivated at the end of your 3rd year (usually the toughest, in India) to go to graduate school in Physics, dive right in! [It is also important to emphasize the need to do well in your undergrad courses -- even the non-physics ones.]