HBO is concerned about injuries on the set of their award winning fantasy series Game of Thrones. Star characters are given real swords which have a point of balance (centre of mass) 5.0cm above the top of the handle. For safety reasons, you are given only the 15cm long, 0.25kg uniform handle and are told to modify it such that the point of balance is shifted to top of the handle. You are told that you are only allowed to add a dense mass to the bottom of the handle and that the blade component is uniform and 90cm long. To assemble the sword, the blade is inserted into the handle and spans the full length. A guard separating the exposed portion of the blade and the handle is also present; length-wise, it is negligibly thin but weighs 0.50kg. How much mass do you add?
I know I have to use the centre of mass equation somehow...