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The pulley shown in figure has a moment ...

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.

Text Solution

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