A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R Figure. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on te tableare connected through a string going over the pulley. Initially the masses are held by a personwith the strings aslong teh outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the mases as seen from the cabin and the tension in the starting.

Explanation

We will solve this this problem in the frame of reference attached to the table. Apply pseudo force on the blocks in outward direction and solve in usual manner.
`3momega^(2)R-T=3ma` ….`(i)`
`T-2momega^(2)R=2ma` ..`(ii)`
From (i) and (ii), we get
`(3momega^(2)R-T)/(T-2momega^(2)R)=(3)/(2)implies6momega^(2)R-2T=3T-6momega^(2)R`
`5T=12 momega^(2)R`
`T=(12)/(5)momega^(2)R`