It depends on your definition of "forced," but I could argue that any mandatory examination is by nature forced. Whenever a physical exam is compulsory, it was not your decision and you would not be there otherwise, so you are being forced. That can happen in several institutions, such as the military, prison and even school or employment. Using that definition, I can say I've had forced exams, and here are notable examples:
1. Military. Mandatory for every man in Brazil the year he turns 18. Unlike men in the US and other countries who may volunteer and then have an entry exam, thousands of young Brazilian boys MUST submit to an exam, usually as a group and often in the nude depending on the town and military branch. Most boys are terrified of that day both from the nudity and humiliation aspect and the possibility to be drafted into the military. In my case, I was in large group of more than 50 guys and we were ordered to strip to underwear. We went through stations for vision, heart, etc and the final one was a line-up when the doctor went one by one, asked to drop underwear and blow on the hand to check for varicocele. However I've heard from friends at the time that had to be completely naked from the start in big group. I don't know anyone who would choose to experience that.
2. College PE. Strange as it may seem, I consider my college PE exams were forced and even worse than the military. At my university you HAD to take two semesters of physical education (PE) and in order to enroll in the PE class, you HAD to have a physical. It was done in group and fully nude for men. The doctor was extremely rude and didn't mince words when barking orders. When he came to the room, he simply shouted "naked, with form in hand" and left. Everybody kept their underwear on and when he came back he was very angry and shouted again: "did I stutter, I said naked with form in hand!!!"
3. Others. I've had two other mandatory exams that I would not classify as forced because they were formalities and there was no nudity or any other "traumatic" aspect. They were pre-employment physical and Green-card physical (United States permanent residency). Both times were quick, individual and cordial. They were more about filing paperwork and the doctors were not high on the power given by the situation.