when should we use centripital acceleration formula of mv^2/r and v^2/r
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Acceleration is either linear or centripetal or angular, now if the speed of an object is changing and the direction is constant then this is a linear acceleration, if the speed of an object is constant and the direction is changing then this is centripetal acceleration, but if both speed and direction are changing then the its an angular acceleration.
now know these things are important to answer your main question
if you recall the way centripetal acceleration is derived, you notice that you have a tangential velocity moving on a curve of radius r, and we have two forces acting one each other then it is important to use the equation with the mass, this is proven by the derivation of the formula
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and this why it is very important to understand every step of deriving a formula
usually question with tensions, satellite navigation, ...etc you will use the the formula of the mass, but questions like car moving and likewise questions you don't really need to include the mass formula of centripetal acceleration, but in real world you need to take into account all the formulas, but at your level keep things simple.