The computer is not really any more protected against a power surge when in hibernation than when running, and a power cut may well be linked to a surge. However,it is much, much less likely to suffer damage due to data loss than if left running. Safest: put into hibernation, then pull the plug!
But pulling the plug is the only safe (cheap) way to avoid surges. Power cuts in villages, at least, are often accompanied by a large surge. Shut down or hibernated, if there's a surge, you'll risk damage to the computer.
There is no different risk from a power cut alone when turned off or hibernating: the power cut will do no damage in either case.
Invest in a UPS which gives time to shut down the PC safely if there is a powercut. This will protect your system while you are working on it. If leaving it and you are worried about it then shut it down.
I'm with MAT ALAN on this one - pulling the plug makes being in hibernation pointless. I agree that "pulling the Plug" is the only way to avoid power surges, but only after shutting down your PC to avoid destabilising Windows.
The point is it makes no difference whether a computer is hibernated or turned off when you pull the plug.
The original question was: If my computer is in hibernation mode and there is a power cut to the computer will there be any possibility of damage.
The answer is that a power cut alone will NOT cause damage; it is exactly the same as switching off the mains socket. BUT (and this is the key) there is a REASON for a power cut and, very often, a power cut is accompanied by a surge. Some are spectacular and take out whole streets or even grid areas. Transformers that fail often trigger such surges, as do the switching mechanisms that automatically cut in to try to restore power.
Should you be in an area heavily prone to power cuts, invest in a surge protector. This will give you increased protection (but not 100% guarantee) while your computer is in use. When not in use, pulling the plug is advisable should you be expecting power cuts (i.e., heavy wind or rain)or should you be expecting lightning in your area.
A disadvantage of leaving unplugged is that the motherboard BIOS battery will discharge faster. Contrary to popular belief, the CR2032 on a mobo will trickle charge, so this is not a big problem if the computer is normally plugged in.