A disc of mass `M` has a light, thin string wrapped several times around its circumference. The free end of string is attaced to the ceiling and the disc is released from rest. Find the acceleration of the disc and the tension in the string.

Explanation

We draw the F.B.D of disc assuming tension to be `T`

Applying Newton's Second Law
`sumF=Ma_(CM)=ltMg-T=Ma`
`sumtau_(CM)=I_(CM)*alpha`
`impliesT.R=(MR^(2))/(2)*alpha=(MR(R alpha))/(2)=(Ma)/(2)` [`:' a=alphaR`]
`implies a=(2g)/(3)` and `T=(Mg)/(3)`