This problem is in a GRE exam which I think might have big mistake in forming the answers: A thin uniform steel chain is 10 meters long with a mass density of 2 kg per meter. One end of the chain is attached to a horizontal axle having a radius that is small compared to the length of the chain. If the chain initially hangs vertically, the work required to slowly wind it up on the axle is closest to 1. 100 J 2. 200 J 3. 1,000 J 4. 2,000 J 5. 10,000 J The solution I made is attached in the post or you can download it from this web site: http://www.samer.ws/ChainProblem.pdf IF THE LINK DIDN'T WORK COPY IT AND PASTE IT IN YOUR BROWSER AND TRY AGAIN and the solution people are sharing is here: http://grephysics.net/ans/9277/66 Please check the attachment, the answer should be 500 joules, GRE said it must be 1000J and people did every trick to reach it, Any suggestions?