Question on energy conservation with centripetal acceleratio

[RoboNerd]

Homework Statement

The right answer is E, and I have no idea how to solve this problem.

Please advise on how to proceed. Thanks in advance.

Homework Equations

conservation of mechanical energy??

The Attempt at a Solution

Many attempts were done, but I am lacking on theory with this. How and why should I choose E and eliminate the other answers?

Thanks!

 

[RoboNerd]

UPDATE: I was able to figure out why I and II are wrong, but I am now stuck on roman numeral III.

Thanks in advance for the help

 

[haruspex]

Consider the speed, v, at point B. How does this relate to H? How does it relate to the centripetal force at B?