question_answer

A railway carriage moves over a straight track with acceleration a. Passenger in the carriage drops a stone. What is the acceleration of the stone w.r.t the carriage and the earth?

Answer:

                When a stone is dropped from a railway carriage, it will fall vertically downwards with acceleration due to gravity g. Therefore, with respect to earth, the acceleration of the stone will be g only. Inside the carriage the stone has two accelerations : (i) horizontal acceleration a, due to the motion of the carriage and (ii) vertical ace. due to gravity g. Thus the acceleration of the stone with respect to carriage is \[\sqrt{{{a}^{2}}+{{g}^{2}}}\] .