A table with a smooth horizontal surface is placed in a cabin moving in a circle of large radius R. A small smooth pulley is fixed to the table. Two masses m and 2m on the table are connected by a string over the pulley. Initially the masses are held with the strings along the outward radial direction and then released from rest relative to the cabin. Find their initial acceleration as seen from the cabin and the tension in the string.

Question

G1 Physics · Accepted Answer

In the cabin frame each mass experiences outward centrifugal force proportional to its mass. Writing the two string-direction equations with equal and opposite accelerations and solving gives acceleration magnitude a=ω²R/3 and tension T=4mω²R/3.