"Professor Povey's Perplexing Problems", written by Thomas Povey, is a great book with many intriguing and challenging maths and physics problems. Here, I upload my solution to some of the problems in the book.
This problem is from chapter 10: gravity. This specific question deals with the resolution of two different forces, weight of a bob and string tension. An interesting phenomena that is being dealt in this question is that when I, for example, have a string with a bob hanging at the end of the string, the line (or axis) created by the path of the string will not exactly be the radial axis from the center of the Earth to the center of the bob. This is because, contrary to the simplification that we tend to make that the bob is in an equilibrium state, the bob is in fact not in an equilibrium state because it is moving in a circular path around the Earth as the Earth rotates, and it has a net centripetal force acting towards the center of the circular path (this circular path depends on the latitude, since the closer the bob is to either poles of Earth, the shorter the circular path will be). After deriving an equation for the difference between the two angles (created by the string and that by the center of the Earth to the bob), I calculated that the angle difference on Seoul, South Korea, where I am located on, would be about 0.09534 degrees.
Bibliography (Only the question is from the book; the solution was firstly done by myself and later on checked if it matches Povey's solution in the book)
Povey, T. (2015). Professor Povey's perplexing problems: Pre-university physics and maths puzzles with solutions. London: Oneworld Publications.