A uniform cylider of mass `M` and radius R has a string wrapped around it. The string is held fixed and the cylinder falls vertically, as in figure.
(a). Show that the acceleration of the cylinder is downward with magnitude `a=(2g)/(3)`
(b). Find the tension in the string.

Explanation

`a=(Mg-T)/(M)` ..(i)
`alpha=(TR)/((1)/(2)MR^(2))=(2T)/(MR)` ..(ii)
`a=Ralpha`
Solving these three equation we get
`a=(2g)/(3)` and `T=(Mg)/(3)`