And also, one doubt, I find that I am able to access windows partitions from ubuntu itself, so, if any nasty virus managed to get into linux, will it transfer itself automatically to windows and do its nasty work?
Linux is extremely secure.
So how does Linux handle the threat of viruses? If the source code is public domain knowledge, wouldn't a hacker more easily be able to develop a virus that is targeted against Linux? In theory, a hacker could do that. But he'll have long series of mountains to climb before he can pull it off. The first mountain he'll have to climb is the source code itself, looking for flaws and vulnerabilities. But due to the open-source nature of Linux the source-code has already been proof-read by thousands and thousands of computer programmers who comb through, constantly looking for areas to make improvements to the software and identify potential problems or flaws. Linus' Law (named after Linus Torvalds) states, "Given enough eyeballs, all bugs are shallow." Or more formally: "Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone." So the robustness of the source code comes from a compounded and continuous method of refining done by millions around the world, which makes Linux much more difficult to hack.
The next mountain he could climb is to try and rewrite some source code and sneak a flaw into the official distribution. In order for anything to be included as a part of the official distribution it has to go through very extensive testing that is much more rigorous than the beta testing that Windows goes through. This is because the software is open source and accessable to many more testers; literally thousands more people are able to examine the software with their own fine tooth comb and then report their findings to the group.
But the biggest mountain our poor hacker would have to climb is system administration privileges (also called root level access or Superuser authentication). What this means is, if anybody wants to install a program (such as a virus), modify system critical configurations or settings, or do anything at all that may affect the way the OS runs, a password is required. By default in Windows, all users are given administrator privileges and no password is required to log into the computer or modify system configuration. You could even open the Windows folder and start deleting random files and the operating system would allow it to happen with barely a peep. This is bad design and bad security, which happen to be two flaws you will never ever find on a Linux system. It's simply not built that way.
sudo apt-get install clamav