Can a County Government Require a Salary Employee to for 50 hours per week but only pay 40 hours

IF you are truly a salaried employee AND also meet one or more of the tests or criteria for exemption from overtime which can be found on the U.S. Dept. of Labor website, such as the "executive" exemption (which really should be called the "managerial" exemption, since it applies to non-executive manager), the "administrative employee" exemption, or one of the several "professional" employee exemptions, then they do not have to pay you anything more than your weekly salary. Exempt salaried employees only receive their weekly salary no matter how many hours they work, and regardless of how other employees are paid (there is no requirement for fairness in the law)--all that matters is if you are truly a salaried exempt employee.
The issue then is: are you salaried exempt?
1) You can be salaried but NOT be exempt, if you do not meet one of the overtime exemptions. Go to the USDOL website, look under "overtime," and compare the exemptions to your job. If you don't meet at least one set of criteria, you are non-exempt, and must receive a premium when working more than 40 hours in a week.
2) Even if they call you salaried, if they track your hours and pay you by the hours, so that if you work, for example, 38 hours in a week, you receive a different amount than working 40 hours (i.e. pay varies by hours worked), you are actually an hourly employee. Hourly employees receive overtime when working more than 40 hours in a week and must also be paid for all hours worked.