Physics : Motion in a vertical circle

My handwritten Physics notes on motion in a vertical circle.

Japanese Sec 4 math question

Holy cow. I saw this sec 4 level question from a Japanese forum.
http://www.page.sannet.ne.jp/ikenoue/type2/area/area.html

Apparently its for some entrance exam.

I think the Japs are insane...
My solution provided. The solution on the webpage is different from mine because they
defined the radius of the circle as half r while I defined it as r, but basically the same strategy.