The answer given by you is 100% correct. Why I said N will come into the picture is because, if you consider N, then it is very easy to calculate the centripetal force, which is simply mgcos@-N. However, in problems, they might not give the value of N, so you've got to use different methods, depending on the data given. I asked you to consider N because I thought that this is the first time you are being introduced to this concept, but you've proven that you've jumped a huge leap already!!
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