The pulley shown in figure has a moment of inertia I about it saxis and its radius is R. Find the magnitude of the acceleration of the two blocks. Assume that the string is light and does not slip on the pulley.

Explanation

Suppose the block of mass .M. goes down with an acceleration .a.. The angular acceleration of the pulley is, therefore
`alpha = (a)/(R )`
`Mg-T_(1)=Ma`
`T_(2)-mg=ma`
`T_(1)R-T_(2)R=I alpha = L(a)/(R )`
Solving the equations `a=((M-m)gR^(2))/(I+(M+m)R^(2))`