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Swapnadeep goswami Best Answer
Please keep in mind that dimebsion of Lagrangian is always that of energy and since the dimension of generalized force is equal to the dimension of the Lagrangian, the generalized coordinate must have dimension M^0L^0T^0 as force is the gradient of energy (loosely) and with that in hand use dimension of (p*qdot)= dimension of Lagrangian which gives dimesnion of generalized momentum as ML^2T^-1