Am I obliged to compensate my friend for the mobile phone that broke after falling out of my bag and being run over by a car?

As long as you took the mobile phone from your friend for his benefit, you are a trustee over it and are not liable for it unless you were negligent in its safekeeping, such as placing it in a bag whose strap you know is damaged or not securely fastened, causing it to break or come undone. In that case, you must guarantee the mobile phone to your friend.