The arrangement shown in figure consists of two identical, uniform, solid cylinders, each of mass `m`, on which two light theads are wound symmetrically.
Find the tensions of each thread in the process of motion. The friction in the axle of the upper cylinder is assumed to be absent.

Explanation

For the cylinder from the equation `N_z=Ibeta_z` about its stationary axis of rotation.
`2Tr=(mr^2)/(2)beta` or `beta=(4T)/(mr)` (1)
For the rotation of the lower cylinder from the equation `N_(cz)=I_cbeta_x`
`2Tr=(mr^2)/(2)beta^'` or, `beta^'=(4T)/(mr)=beta`
Now for the translational motion of lower cylinder from the Eq. `F_x=mw_(cx)`:
`mg-2T=mw_c` (2)
As there is no slipping of threads on the cylinders:
`w_c=beta^'r+betar=2betar` (3)
Simultaneous solution of (1), (2) and (3) yields
`T=(mg)/(10)`