By making private constructor, we can avoid instantiating class from anywhere outside. and by making class final, no other class can extend it. Why is it necessary for Util class to have private constructor and final class ?
This is not a mandate from a functional point of view or java complication or runtime. However, it's a coding standard accepted by the wider community. Even most static code review tools, like checkstyle, check that such classes have this convention followed.
Why this convention is followed is already explained in other answers and even OP covered that, but I'd like to explain it a little further.
Mostly utility classes are a collection of methods/functions which are independent of an object instance. Those are kind of like aggregate functions as they depend only on parameters for return values and are not associated with class variables of the utility class. So, these functions/methods are mostly kept static. As a result, utility classes are, ideally, classes with only static methods. Therefore, any programmer calling these methods doesn't need to instantiate the class. However, some robo-coders (maybe with less experience or interest) will tend to create the object as they believe they need to before calling its method. To avoid that, we have 3 options:
Now, if someone wants to add a new method for some functionality to the utility class, they don't need to extend it: they can add a new method as each method is independent and has no chance of breaking other functionalities. So, no need to override it. Also, you are not going to instantiate it, so no need to subclass it. Better to mark it final.
In summary, instantiating a utility class (new MyUtilityClass()) does not make sense. Hence the constructors should be private. And you never want to override or extend it, so mark it final.